
Corrigendum to “Trace spaces of counterexamples to Naimark's problem” [J. Funct. Anal. 275 (10) (2018) 2794–2816] J. Funct. Anal. (IF 1.637) Pub Date : 20200120
Andrea VaccaroBecause of a mistake in the proof of [10, Theorem A  part 1], the main statements of [10] ([10, Theorem 1  part 1] and [10, Theorem 2]) are not proved in full generality. We provide an alternative proof to such statements.

Topological centres of weighted convolution algebras J. Funct. Anal. (IF 1.637) Pub Date : 20200114
Mahmoud Filali; Pekka SalmiLet G be a noncompact locally compact group with a continuous submultiplicative weight function ω such that ω(e)=1 and ω is diagonally bounded with bound K≥1. When G is σcompact, we show that ⌊K⌋+1 many points in the spectrum of LUC(ω−1) are enough to determine the topological centre of LUC(ω−1)⁎ and that ⌊K⌋+2 many points in the spectrum of L∞(ω−1) are enough to determine the topological centre of L1(ω)⁎⁎ when G is in addition a SINgroup. We deduce that the topological centre of LUC(ω−1)⁎ is the weighted measure algebra M(ω) and that of C0(ω−1)⊥ is trivial for any locally compact group. The topological centre of L1(ω)⁎⁎ is L1(ω) and that of of L0∞(ω)⊥ is trivial for any noncompact locally compact SINgroup. The same techniques apply and lead to similar results when G is a weakly cancellative right cancellative discrete semigroup.

Incomplete Yamabe flows and removable singularities J. Funct. Anal. (IF 1.637) Pub Date : 20200114
Mario B. SchulzWe study the Yamabe flow on a Riemannian manifold of dimension m≥3 minus a closed submanifold of dimension n and prove that there exists an instantaneously complete solution if and only if n>m−22. In the remaining cases 0≤n≤m−22 including the borderline case, we show that the removability of the ndimensional singularity is necessarily preserved along the Yamabe flow. In particular, the flow must remain geodesically incomplete as long as it exists. This is contrasted with the twodimensional case, where instantaneously complete solutions always exist.

A Bernstein type theorem for minimal hypersurfaces via Gauss maps J. Funct. Anal. (IF 1.637) Pub Date : 20200114
Qi DingLet M be an ndimensional smooth oriented complete embedded minimal hypersurface in Rn+1 with Euclidean volume growth. We show that if the image under the Gauss map of M avoids some neighborhood of a halfequator, then M must be an affine hyperplane.

A characterization of modulation spaces by symplectic rotations J. Funct. Anal. (IF 1.637) Pub Date : 20200114
Elena Cordero; Maurice de Gosson; Fabio NicolaThis note contains a new characterization of modulation spaces Mmp(Rn), 1≤p≤∞, by symplectic rotations. Precisely, instead to measure the timefrequency content of a function by using translations and modulations of a fixed window as building blocks, we use translations and metaplectic operators corresponding to symplectic rotations. Technically, this amounts to replace, in the computation of the Mmp(Rn)norm, the integral in the timefrequency plane with an integral on Rn×U(2n,R) with respect to a suitable measure, U(2n,R) being the group of symplectic rotations. More conceptually, we are considering a sort of polar coordinates in the timefrequency plane. To have invariance under symplectic rotations we choose a Gaussian as suitable window function. We also provide a similar (and easier) characterization with the group U(2n,R) being reduced to the ndimensional torus Tn.

On the embeddability of the family of countably branching trees into quasireflexive Banach spaces J. Funct. Anal. (IF 1.637) Pub Date : 20200114
Y. PerreauIn this note we extend to the quasireflexive setting the result of F. Baudier, N. Kalton and G. Lancien concerning the nonembeddability of the family of countably branching trees into reflexive Banach spaces whose Szlenk index and Szlenk index from the dual are both equal to the first infinite ordinal ω. In particular we show that the family of countably branching trees does neither embed into the James space Jp nor into its dual space Jp⁎ for p∈(1,∞).

Tempered distributions and Schwartz functions on definable manifolds J. Funct. Anal. (IF 1.637) Pub Date : 20200114
Ary ShavivWe define the spaces of Schwartz functions, tempered functions and tempered distributions on manifolds definable in polynomially bounded ominimal structures. We show that all the classical properties that these spaces have in the Nash category, as first studied in Fokko du Cloux's work, also hold in this generalized setting. We also show that on manifolds definable in ominimal structures that are not polynomially bounded, such a theory can not be constructed. We present some possible applications, mainly in representation theory.

Difference equations and pseudodifferential operators on Zn J. Funct. Anal. (IF 1.637) Pub Date : 20200114
Linda N.A. Botchway; P. Gaël Kibiti; Michael RuzhanskyIn this paper we develop the calculus of pseudodifferential operators on the lattice Zn, which we can call pseudodifference operators. An interesting feature of this calculus is that the global frequency space (Tn) is compact so the symbol classes are defined in terms of the behaviour with respect to the lattice variable. We establish formulae for composition, adjoint, transpose, and for parametrix for the elliptic operators. We also give conditions for the ℓ2, weighted ℓ2, and ℓp boundedness of operators and for their compactness on ℓp. We describe a link to the toroidal quantization on the torus Tn, and apply it to give conditions for the membership in Schatten classes on ℓ2(Zn). Furthermore, we discuss a version of Fourier integral operators on the lattice and give conditions for their ℓ2boundedness. The results are applied to give estimates for solutions to difference equations on the lattice Zn. Moreover, we establish Gårding and sharp Gårding inequalities, with an application to the unique solvability of parabolic equations on the lattice Zn.

Bianalytic free maps between spectrahedra and spectraballs J. Funct. Anal. (IF 1.637) Pub Date : 20200114
J. William Helton; Igor Klep; Scott McCullough; Jurij VolčičLinear matrix inequalities (LMIs) are ubiquitous in real algebraic geometry, semidefinite programming, control theory and signal processing. LMIs with (dimension free) matrix unknowns are central to the theories of completely positive maps and operator algebras, operator systems and spaces, and serve as the paradigm for matrix convex sets. The matricial feasibility set of an LMI is called a free spectrahedron. In this article, the bianalytic maps between a very general class of balllike free spectrahedra (examples of which include row or column contractions, and tuples of contractions) and arbitrary free spectrahedra are characterized and seen to have an elegant algebraic form. They are all highly structured rational maps. In the case that both the domain and codomain are balllike, these bianalytic maps are explicitly determined and the article gives necessary and sufficient conditions for the existence of such a map with a specified value and derivative at a point. In particular, this result leads to a classification of automorphism groups of balllike free spectrahedra. The proofs depend on a novel free Nullstellensatz, established only after new tools in free analysis are developed and applied to obtain fine detail, geometric in nature locally and algebraic in nature globally, about the boundary of balllike free spectrahedra.

Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities J. Funct. Anal. (IF 1.637) Pub Date : 20200110
Patricia Alonso Ruiz; Fabrice Baudoin; Li Chen; Luke G. Rogers; Nageswari Shanmugalingam; Alexander TeplyaevWe introduce heat semigroupbased Besov classes in the general framework of Dirichlet spaces. General properties of those classes are studied and quantitative regularization estimates for the heat semigroup in this scale of spaces are obtained. As a highlight of the paper, we obtain a far reaching Lpanalogue, p≥1, of the Sobolev inequality that was proved for p=2 by N. Varopoulos under the assumption of ultracontractivity for the heat semigroup. The case p=1 is of special interest since it yields isoperimetric type inequalities.

Magic identities for the conformal fourpoint integrals; the Minkowski metric case J. Funct. Anal. (IF 1.637) Pub Date : 20191113
Matvei LibineThe original “magic identities” are due to J. M. Drummond, J. Henn, V. A. Smirnov and E. Sokatchev; they assert that all nloop box integrals for four scalar massless particles are equal to each other [3]. The authors give a proof of the magic identities for the Euclidean metric case only and claim that the result is also true in the Minkowski metric. However, the Minkowski case is much more subtle and requires specification of the relative positions of cycles of integration to make these identities correct. In this article we prove the magic identities in the Minkowski metric case and, in particular, specify the cycles of integration. Our proof of magic identities relies on previous results from [7], [8], where we give a mathematical interpretation of the nloop box integrals in the context of representations of a Lie group U(2,2) and quaternionic analysis. The main result of [7], [8] is a (weaker) operator version of the “magic identities”. No prior knowledge of physics or Feynman diagrams is assumed from the reader. We provide a summary of all relevant results from quaternionic analysis to make the article selfcontained.

Uniqueness properties of solutions to the BenjaminOno equation and related models J. Funct. Anal. (IF 1.637) Pub Date : 20191113
C.E. Kenig; G. Ponce; L. VegaWe prove that if u1,u2 are real solutions of the BenjaminOno equation defined in (x,t)∈R×[0,T] which agree in an open set Ω⊂R×[0,T], then u1≡u2. We extend this uniqueness result to a general class of equations of BenjaminOno type in both the initial value problem and the initial periodic boundary value problem. This class of 1dimensional nonlocal models includes the intermediate long wave equation. We relate our uniqueness results with those for a water wave problem. Finally, we present a slightly stronger version of our uniqueness results for the BenjaminOno equation.

An extension problem related to the fractional Branson–Gover operators J. Funct. Anal. (IF 1.637) Pub Date : 20191113
Jan Frahm; Bent Ørsted; Genkai ZhangThe Branson–Gover operators are conformally invariant differential operators of even degree acting on differential forms. They can be interpolated by a holomorphic family of conformally invariant integral operators called fractional Branson–Gover operators. For Euclidean spaces we show that the fractional Branson–Gover operators can be obtained as DirichlettoNeumann operators of certain conformally invariant boundary value problems, generalizing the work of Caffarelli–Silvestre for the fractional Laplacians to differential forms. The relevant boundary value problems are studied in detail and we find appropriate Sobolev type spaces in which there exist unique solutions and obtain the explicit integral kernels of the solution operators as well as some of their properties.

Pointwise gradient estimates for a class of singular quasilinear equations with measure data J. Funct. Anal. (IF 1.637) Pub Date : 20191112
QuocHung Nguyen; Nguyen Cong PhucLocal and global pointwise gradient estimates are obtained for solutions to the quasilinear elliptic equation with measure data −div(A(x,∇u))=μ in a bounded and possibly nonsmooth domain Ω in Rn. Here div(A(x,∇u)) is modeled after the pLaplacian. Our results extend earlier known results to the singular case in which 3n−22n−1

Characterization of initial data in the homogeneous Besov space for solutions in the Serrin class of the NavierStokes equations J. Funct. Anal. (IF 1.637) Pub Date : 20191113
Hideo Kozono; Akira Okada; Senjo ShimizuConsider the Cauchy problem of the NavierStokes equations in Rn with initial data a in the homogeneous Besov space B˙p,q−1+np(Rn) for n

Incompressible inhomogeneous fluids in bounded domains of R3 with bounded density J. Funct. Anal. (IF 1.637) Pub Date : 20191112
Reinhard Farwig; Chenyin Qian; Ping ZhangIn this paper, we study the incompressible inhomogeneous NavierStokes equations in bounded domains of R3 involving bounded density functions ρ=1+a. Based on the corresponding theory of Besov spaces on domains, we first obtain the global existence of weak solutions (ρ,u) with initial data a0∈L∞(Ω), u0∈Bq,s−1+3/q(Ω) for 1

Prime II1 factors arising from actions of product groups J. Funct. Anal. (IF 1.637) Pub Date : 20191024
Daniel DrimbeWe prove that any II1 factor arising from a free ergodic probability measure preserving action Γ↷X of a product Γ=Γ1×…×Γn of icc hyperbolic, free product or wreath product groups is prime, provided Γi↷X is ergodic, for any 1≤i≤n. We also completely classify all the tensor product decompositions of a II1 factor associated to a free ergodic probability measure preserving action of a product of icc, hyperbolic, property (T) groups. As a consequence, we derive a unique prime factorization result for such II1 factors. Finally, we obtain a unique prime factorization theorem for a large class of II1 factors which have property Gamma.

Difference of weighted composition operators J. Funct. Anal. (IF 1.637) Pub Date : 20191113
Boo Rim Choe; Koeun Choi; Hyungwoon Koo; Jongho YangWe obtain complete characterizations in terms of Carleson measures for bounded/compact differences of weighted composition operators acting on the standard weighted Bergman spaces over the unit disk. Unlike the known results, we allow the weight functions to be nonholomorphic and unbounded. As a consequence we obtain a compactness characterization for differences of unweighted composition operators acting on the Hardy spaces in terms of Carleson measures and, as a nontrivial application of this, we show that compact differences of composition operators with univalent symbols on the Hardy spaces are exactly the same as those on the weighted Bergman spaces. As another application, we show that an earlier characterization due to Acharyya and Wu for compact differences of weighted composition operators with bounded holomorphic weights does not extend to the case of nonholomorphic weights. We also include some explicit examples related to our results.

Analytic and algebraic indices of elliptic operators associated with discrete groups of quantized canonical transformations J. Funct. Anal. (IF 1.637) Pub Date : 20191113
Anton Savin; Elmar SchroheWe consider elliptic operators associated with discrete groups of quantized canonical transformations. In order to be able to apply results from algebraic index theory, we define the localized algebraic index of the complete symbol of an elliptic operator. With the help of a calculus of semiclassical quantized canonical transformations, a version of Egorov's theorem and a theorem on trace asymptotics for semiclassical Fourier integral operators we show that the localized analytic index and the localized algebraic index coincide. As a corollary, we express the Fredholm index in terms of the algebraic index for a wide class of groups, in particular, for finite extensions of Abelian groups.

Inversion problem in measure and Fourier–Stieltjes algebras J. Funct. Anal. (IF 1.637) Pub Date : 20191113
Przemysław Ohrysko; Mateusz WasilewskiIn this paper we study the inversion problem in measure and Fourier–Stieltjes algebras from qualitative and quantitative point of view extending the results obtained by N. Nikolski in [10].

Compact linear combination of composition operators on Bergman spaces J. Funct. Anal. (IF 1.637) Pub Date : 20191113
Boo Rim Choe; Hyungwoon Koo; Maofa WangMotivated by the question of Shapiro and Sundberg raised in 1990, study on linear combinations of composition operators has been a topic of growing interest. In this paper, we completely characterize the compactness of any finite linear combination of composition operators with general symbols on the weighted Bergman spaces in two classical terms: one is a function theoretic characterization of JuliaCarathéodory type and the other is a measure theoretic characterization of Carleson type. Our approach is completely different from what has been known so far.

Bibasic sequences in Banach lattices J. Funct. Anal. (IF 1.637) Pub Date : 20200103
M.A. Taylor; V.G. TroitskyGiven a Schauder basic sequence (xk) in a Banach lattice, we say that (xk) is bibasic if the expansion of every vector in [xk] converges not only in norm, but also in order. We prove that, in this definition, order convergence may be replaced with uniform convergence, with order boundedness of the partial sums, or with norm boundedness of finite suprema of the partial sums. The results in this paper extend and unify those from the pioneering paper Order Schauder bases in Banach lattices by A. Gumenchuk, O. Karlova, and M. Popov. In particular, we are able to characterize bibasic sequences in terms of the bibasis inequality, a result they obtained under certain additional assumptions. After establishing the aforementioned characterizations of bibasic sequences, we embark on a deeper study of their properties. We show, for example, that they are independent of ambient space, stable under small perturbations, and preserved under sequentially uniformly continuous norm isomorphic embeddings. After this we consider several special kinds of bibasic sequences, including permutable sequences, i.e., sequences for which every permutation is bibasic, and absolute sequences, i.e., sequences where expansions remain convergent after we replace every term with its modulus. We provide several equivalent characterizations of absolute sequences, showing how they relate to bibases and to further modifications of the basis inequality. We further consider bibasic sequences with unique order expansions. We show that this property does generally depend on ambient space, but not for the inclusion of c0 into ℓ∞. We also show that small perturbations of bibases with unique order expansions have unique order expansions, but this is not true if “bibases” is replaced with “bibasic sequences”. In the final section, we consider uobibasic sequences, which are obtained by replacing order convergence with uoconvergence in the definition of a bibasic sequence. We show that such sequences are very common.

Normsquare localization and the quantization of Hamiltonian loop group spaces J. Funct. Anal. (IF 1.637) Pub Date : 20200103
Yiannis Loizides; Yanli SongIn an earlier article we introduced a new definition for the ‘quantization’ of a Hamiltonian loop group space M, involving the equivariant L2index of a Diractype operator D on a noncompact finite dimensional submanifold Y of M. In this article we study a deformation of this operator, similar to the work of TianZhang and MaZhang. We obtain a formula for the index with infinitely many nontrivial contributions, indexed by the components of the critical set of the normsquare of the moment map. This is the main part of a new proof of the [Q,R]=0 theorem for Hamiltonian loop group spaces.

Weak and strong type estimates for the multilinear pseudodifferential operators J. Funct. Anal. (IF 1.637) Pub Date : 20200103
Mingming Cao; Qingying Xue; Kôzô YabutaIn this paper, we investigate the boundedness of the multilinear pseudodifferential operator Tσ. First, we establish the local exponential decay estimates for Tσ. In terms of the corresponding commutators Tσ,Σb, we obtain the local subexponential decay estimates. Secondly, we derive the weighted mixed weak type inequality for Tσ, which parallels Sawyer's conjecture for CalderónZygmund operators and covers the endpoint weighted inequalities. Last but not least, we present the sharp weighted estimates for Tσ and Tσ,Σb. It is worth mentioning that our results are totally new even in the linear case.

Operatorvalued chordal Loewner chains and noncommutative probability J. Funct. Anal. (IF 1.637) Pub Date : 20200103
David JekelWe adapt the theory of chordal Loewner chains to the operatorvalued matricial upperhalf plane over a C⁎algebra A. We define an Avalued chordal Loewner chain as a subordination chain of analytic selfmaps of the Avalued upper halfplane, such that each Ft is the reciprocal Cauchy transform of an Avalued law μt, such that the mean and variance of μt are continuous functions of t. We relate Avalued Loewner chains to processes with Avalued free or monotone independent independent increments just as was done in the scalar case by Bauer [1] and Schleißinger [2]. We show that the Loewner equation ∂tFt(z)=DFt(z)[Vt(z)], when interpreted in a certain distributional sense, defines a bijection between Lipschitz meanzero Loewner chains Ft and vector fields Vt(z) of the form Vt(z)=−Gνt(z) where νt is a generalized Avalued law. Based on the Loewner equation, we derive a combinatorial expression for the moments of μt in terms of νt. We also construct noncommutative random variables on an operatorvalued monotone Fock space which realize the laws μt. Finally, we prove a version of the monotone central limit theorem which describes the behavior of Ft as t→+∞ when νt has uniformly bounded support.

Radiation condition bounds on manifolds with ends J. Funct. Anal. (IF 1.637) Pub Date : 20200103
K. Ito; E. SkibstedWe study spectral theory for the Schrödinger operator on manifolds possessing an escape function. A particular class of examples are manifolds with Euclidean and/or hyperbolic ends. Certain exterior domains for possibly unbounded obstacles are included. We prove Rellich's theorem, the limiting absorption principle, radiation condition bounds and the Sommerfeld uniqueness result, striving to extending and refining previously known spectral results on manifolds. The proofs are given by an extensive use of commutator arguments. These arguments have a classical spirit (essentially) not involving energy cutoffs or microlocal analysis and require, presumably, minimum regularity and decay properties of perturbations. This paper has interest of its own right, but it also serves as a basis for the stationary scattering theory developed fully in the sequel [20].

On boundedness and compactness of Toeplitz operators in weighted H∞spaces J. Funct. Anal. (IF 1.637) Pub Date : 20200102
José Bonet; Wolfgang Lusky; Jari TaskinenWe characterize the boundedness and compactness of Toeplitz operators Ta with radial symbols a in weighted H∞spaces Hv∞ on the open unit disc of the complex plane. The weights v are also assumed radial and to satisfy the condition (B) introduced by the second named author. The main technique uses Taylor coefficient multipliers, and the results are first proved for them. We formulate a related sufficient condition for the boundedness and compactness of Toeplitz operators in reflexive weighted Bergman spaces on the disc. We also construct a bounded harmonic symbol f such that Tf is not bounded in Hv∞ for any v satisfying mild assumptions. As a corollary, the Bergman projection is never bounded with respect to the corresponding weighted supnorms. However, we also show that, for normal weights v, all Toeplitz operators with a trigonometric polynomial as the symbol are bounded on Hv∞.

Superlinear elliptic inequalities on manifolds J. Funct. Anal. (IF 1.637) Pub Date : 20200102
Alexander Grigor'yan; Yuhua Sun; Igor VerbitskyLet M be a complete noncompact Riemannian manifold and let σ be a Radon measure on M. We study the problem of existence or nonexistence of positive solutions to a semilinear elliptic inequaliy−Δu≥σuqinM, where q>1. We obtain necessary and sufficent criteria for existence of positive solutions in terms of Green function of Δ. In particular, explicit necessary and sufficient conditions are given when M has nonnegative Ricci curvature everywhere in M, or more generally when Green's function satisfies the 3Ginequality.

Asymptotics of Cheeger constants and unitarisability of groups J. Funct. Anal. (IF 1.637) Pub Date : 20200102
Maria Gerasimova; Dominik Gruber; Nicolas Monod; Andreas ThomGiven a group Γ, we establish a connection between the unitarisability of its uniformly bounded representations and the asymptotic behaviour of the isoperimetric constants of Cayley graphs of Γ for increasingly large generating sets. The connection hinges on an analytic invariant Lit(Γ)∈[0,∞] which we call the Littlewood exponent. Finiteness, amenability, unitarisability and the existence of free subgroups are related respectively to the thresholds 0,1,2 and ∞ for Lit(Γ). Using graphical small cancellation theory, we prove that there exist groups Γ for which 1

Nonlinear operations on a class of modulation spaces J. Funct. Anal. (IF 1.637) Pub Date : 20200102
Tomoya Kato; Mitsuru Sugimoto; Naohito TomitaWe discuss when the nonlinear operation f↦F(f) maps the modulation space Msp,q(Rn) (1≤p,q≤∞) to the same space again. It is known that Msp,q(Rn) is a multiplication algebra when s>n−n/q, hence it is true for this space if F is entire. We claim that it is still true for nonanalytic F when q≥4/3.

Spectral enclosures for a class of block operator matrices J. Funct. Anal. (IF 1.637) Pub Date : 20200102
Juan Giribet; Matthias Langer; Francisco Martínez Pería; Friedrich Philipp; Carsten TrunkWe prove new spectral enclosures for the nonreal spectrum of a class of 2×2 block operator matrices with selfadjoint operators A and D on the diagonal and operators B and −B⁎ as offdiagonal entries. One of our main results resembles Gershgorin's circle theorem. The enclosures are applied to Jframe operators.

A formula for the anisotropic total variation of SBV functions J. Funct. Anal. (IF 1.637) Pub Date : 20200102
Fernando Farroni; Nicola Fusco; Serena Guarino Lo Bianco; Roberta SchiattarellaThe purpose of this paper is to present the relation between certain BMO–type seminorms and the total variation of SBV functions. Following some ideas of [2], we give a representation formula of the total variation of SBV functions which does not make use of the distributional derivatives. We consider an anisotropic variant of the BMO–type seminorm introduced in [4], by using, instead of cubes, covering families made by translations of a given open bounded set with Lipschitz boundary.

Finite field restriction estimates for the paraboloid in high even dimensions J. Funct. Anal. (IF 1.637) Pub Date : 20200102
Alex Iosevich; Doowon Koh; Mark LewkoWe prove that the finite field Fourier extension operator for the paraboloid is bounded from L2→Lr for r≥2d+4d in even dimensions d≥8, which is the optimal L2 estimate. For d=6 we obtain the optimal range r>2d+4d=8/3, apart from the endpoint. For d=4 we improve the prior range of r>16/5=3.2 to r≥28/9=3.111…, compared to the conjectured range of r≥3. The key new ingredient is improved additive energy estimates for subsets of the paraboloid.

Lifting for manifoldvalued maps of bounded variation J. Funct. Anal. (IF 1.637) Pub Date : 20200102
Giacomo Canevari; Giandomenico OrlandiLet N be a smooth, compact, connected Riemannian manifold without boundary. Let E→N be the Riemannian universal covering of N. For any bounded, smooth domain Ω⊆Rd and any u∈BV(Ω,N), we show that u has a lifting v∈BV(Ω,E). Our result proves a conjecture by Bethuel and Chiron.

Distribution of scattering resonances for generic Schrödinger operators J. Funct. Anal. (IF 1.637) Pub Date : 20200102
TienCuong Dinh; ViêtAnh NguyênLet −Δ+V be the Schrödinger operator acting on L2(Rd,C) with d≥3 odd. Here V is a bounded real or complexvalued function vanishing outside the closed ball of center 0 and radius a. If V belongs to the class Ma of potentials introduced by Christiansen, we show that when r→∞, the resonances of −Δ+V, scaled down by the factor r, are asymptotically distributed, with respect to an explicit probability distribution on the lower unit halfdisc of the complex plane. The rate of convergence is also considered for subclasses of potentials.

Schauder estimates for drifted fractional operators in the supercritical case J. Funct. Anal. (IF 1.637) Pub Date : 20191219
PaulÉric Chaudru de Raynal; Stéphane Menozzi; Enrico PriolaWe consider a nonlocal operator Lα which is the sum of a fractional Laplacian △α/2, α∈(0,1), plus a first order term which is measurable in the time variable and locally βHölder continuous in the space variables. Importantly, the fractional Laplacian Δα/2 does not dominate the first order term. We show that global parabolic Schauder estimates hold even in this case under the natural condition α+β>1. Thus, the constant appearing in the Schauder estimates is in fact independent of the L∞norm of the first order term. In our approach we do not use the socalled extension property and we can replace △α/2 with other operators of αstable type which are somehow close, including the relativistic αstable operator. Moreover, when α∈(1/2,1), we can prove Schauder estimates for more general αstable type operators like the singular cylindrical one, i.e., when △α/2 is replaced by a sum of one dimensional fractional Laplacians ∑k=1d(∂xkxk2)α/2.

On families of optimal Hardyweights for linear secondorder elliptic operators J. Funct. Anal. (IF 1.637) Pub Date : 20191213
Yehuda Pinchover; Idan VersanoWe construct families of optimal Hardyweights for a subcritical linear secondorder elliptic operator using a onedimensional reduction. More precisely, we first characterize all optimal Hardyweights with respect to onedimensional subcritical SturmLiouville operators on (a,b), ∞≤a

FaberKrahn type inequalities and uniqueness of positive solutions on metric measure spaces J. Funct. Anal. (IF 1.637) Pub Date : 20191213
Anup Biswas; Janna LierlWe consider a general class of metric measure spaces equipped with a strongly local regular Dirichlet form and provide a lower bound on the hitting time probabilities of the associated Hunt process. Using these estimates we establish (i) a generalization of the classical Lieb's inequality, and (ii) uniqueness of nonnegative supersolutions to semilinear elliptic equations on metric measure spaces. Finally, using heatkernel estimates we generalize the local FaberKrahn inequality recently obtained in [28] to local and nonlocal Dirichlet spaces.

Decomposing algebraic misometric tuples J. Funct. Anal. (IF 1.637) Pub Date : 20191213
Trieu LeWe show that any misometric tuple of commuting algebraic operators on a Hilbert space can be decomposed as a sum of a spherical isometry and a commuting nilpotent tuple. Our approach applies as well to tuples of algebraic operators that are hereditary roots of polynomials in several variables.

Automorphic equivalence within gapped phases in the bulk J. Funct. Anal. (IF 1.637) Pub Date : 20191213
Alvin Moon; Yoshiko OgataWe develop a new adiabatic theorem for unique gapped ground states which does not require the gap for local Hamiltonians. We instead require a gap in the bulk and a smoothness of expectation values of subexponentially localized observables in the unique gapped ground state φs(A). This requirement is weaker than the requirement of the gap of the local Hamiltonians, since a uniform spectral gap for finite dimensional ground states implies a gap in the bulk for unique gapped ground states, as well as the smoothness.

An operatorvalued T1 theory for symmetric CZOs J. Funct. Anal. (IF 1.637) Pub Date : 20191213
Guixiang Hong; Honghai Liu; Tao MeiWe provide a natural BMOcriterion for the L2boundedness of CalderónZygmund operators with operatorvalued kernels satisfying a symmetric property. Our arguments involve both classical and quantum probability theory. In the appendix, we give a proof of the L2boundedness of the commutators [Rj,b] whenever b belongs to the Bourgain's vectorvalued BMO space, where Rj is the jth Riesz transform. A common ingredient is the operatorvalued Haar multiplier studied by Blasco and Pott.

Propagation in a FisherKPP equation with nonlocal advection J. Funct. Anal. (IF 1.637) Pub Date : 20191213
François Hamel; Christopher HendersonWe investigate the influence of a general nonlocal advection term of the form K⁎u to propagation in the onedimensional FisherKPP equation. This model is a generalization of the KellerSegelFisher system. When K∈L1(R), we obtain explicit upper and lower bounds on the propagation speed which are asymptotically sharp and more precise than previous works. When K∈Lp(R) with p>1 and is nonincreasing in (−∞,0) and in (0,+∞), we show that the position of the “front” is of order O(tp) if p<∞ and O(eλt) for some λ>0 if p=∞ and K(+∞)>0. We use a wide range of techniques in our proofs.

The SegalBargmann transform on classical matrix Lie groups J. Funct. Anal. (IF 1.637) Pub Date : 20191213
Alice Z. ChanWe study the complextime SegalBargmann transform Bs,τKN on a compact type Lie group KN, where KN is one of the following classical matrix Lie groups: the special orthogonal group SO(N,R), the special unitary group SU(N), or the compact symplectic group Sp(N). Our work complements and extends the results of Driver, Hall, and Kemp on the SegalBargman transform for the unitary group U(N). We provide an effective method of computing the action of the SegalBargmann transform on trace polynomials, which comprise a subspace of smooth functions on KN extending the polynomial functional calculus. Using these results, we show that as N→∞, the finitedimensional transform Bs,τKN has a meaningful limit Gs,τ which can be identified as an operator on the space of complex Laurent polynomials.

On the convergence of stationary solutions in the SmoluchowskiKramers approximation of infinite dimensional systems J. Funct. Anal. (IF 1.637) Pub Date : 20191213
Sandra Cerrai; Nathan GlattHoltzWe prove the convergence, in the small mass limit, of statistically invariant states for a class of semilinear damped wave equations, perturbed by an additive Gaussian noise, both with Lipschitzcontinuous and with polynomial nonlinearities. In particular, we prove that the first marginals of any sequence of invariant measures for the stochastic wave equation converge in a suitable Wasserstein metric to the unique invariant measure of the limiting stochastic semilinear parabolic equation obtained in the SmoluchowskiKramers approximation. The Wasserstein metric is associated to a suitable distance on the space of square integrable functions, that is chosen in such a way that the dynamics of the limiting stochastic parabolic equation is contractive with respect to such a Wasserstein metric. This implies that the limiting result is a consequence of the validity of a generalized SmoluchowskiKramers limit at fixed times. The proof of such a generalized limit requires new delicate bounds for the solutions of the stochastic wave equation, that must be uniform with respect to the size of the mass.

Maximal function characterizations for Hardy spaces on spaces of homogeneous type with finite measure and applications J. Funct. Anal. (IF 1.637) Pub Date : 20191213
The Anh Bui; Xuan Thinh Duong; Fu Ken LyWe prove nontangential and radial maximal function characterizations for Hardy spaces associated to a nonnegative selfadjoint operator satisfying Gaussian estimates on a space of homogeneous type with finite measure. This not only addresses an open point in the literature, but also gives a complete answer to the question posed by Coifman and Weiss in the case of finite measure. We then apply our results to give maximal function characterizations for Hardy spaces associated to second–order elliptic operators with Neumann and Dirichlet boundary conditions, Schrödinger operators with Dirichlet boundary conditions, and Fourier–Bessel operators.

Algebras of noncommutative functions on subvarieties of the noncommutative ball: The bounded and completely bounded isomorphism problem J. Funct. Anal. (IF 1.637) Pub Date : 20191213
Guy Salomon; Orr M. Shalit; Eli ShamovichGiven a noncommutative (nc) variety V in the nc unit ball Bd, we consider the algebra H∞(V) of bounded nc holomorphic functions on V. We investigate the problem of when two algebras H∞(V) and H∞(W) are isomorphic. We prove that these algebras are weak⁎ continuously isomorphic if and only if there is an nc biholomorphism G:W˜→V˜ between the similarity envelopes that is biLipschitz with respect to the free pseudohyperbolic metric. Moreover, such an isomorphism always has the form f↦f∘G, where G is an nc biholomorphism. These results also shed some new light on automorphisms of the noncommutative analytic Toeplitz algebras H∞(Bd) studied by Davidson–Pitts and by Popescu. In particular, we find that Aut(H∞(Bd)) is a proper subgroup of Aut(B˜d). When d<∞ and the varieties are homogeneous, we remove the weak⁎ continuity assumption, showing that two such algebras are boundedly isomorphic if and only if there is a biLipschitz nc biholomorphism between the similarity envelopes of the nc varieties. We provide two proofs. In the noncommutative setting, our main tool is the noncommutative spectral radius, about which we prove several new results. In the free commutative case, we use a new free commutative Nullstellensatz that allows us to bootstrap techniques from the fully commutative case.

Some rigidity results for II1 factors arising from wreath products of property (T) groups J. Funct. Anal. (IF 1.637) Pub Date : 20191127
Ionut Chifan; Bogdan Teodor UdreaWe show that any infinite collection (Γn)n∈N of icc, hyperbolic, property (T) groups satisfies the following von Neumann algebraic infinite product rigidity phenomenon. If Λ is an arbitrary group such that L(⊕n∈NΓn)≅L(Λ) then there exists an infinite direct sum decomposition Λ=(⊕n∈NΛn)⊕A with A icc amenable or trivial such that, for all n∈N, up to amplifications, we have L(Γn)≅L(Λn) and L(⊕k≥nΓk)≅L((⊕k≥nΛk)⊕A). The result is sharp and complements the previous finite product rigidity property found in [16]. Using this we provide an uncountable family of restricted wreath products Γ≅Σ≀Δ of icc, property (T) groups Σ, Δ whose wreath product structure is recognizable, up to a normal amenable subgroup, from their von Neumann algebras L(Γ). Along the way we highlight several applications of these results to the study of rigidity in the C⁎algebra setting.

Matrix elements of irreducible representations of SU(n + 1)×SU(n + 1) and multivariable matrixvalued orthogonal polynomials J. Funct. Anal. (IF 1.637) Pub Date : 20191127
Erik Koelink; Maarten van Pruijssen; Pablo RománIn Part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules. The spherical functions are taking values in the spaces of linear operators of a finite dimensional representation of the subgroup, so the spherical functions are matrixvalued. Under these assumptions these functions can be described in terms of matrixvalued orthogonal polynomials in several variables, where the number of variables is the rank of the compact symmetric pair. Moreover, these polynomials are uniquely determined as simultaneous eigenfunctions of a commutative algebra of differential operators. In Part 2 we verify that the group case SU(n+1) meets all the conditions that we impose in Part 1. For any k∈N0 we obtain families of orthogonal polynomials in n variables with values in the N×Nmatrices, where N=(n+kk). The case k=0 leads to the classical HeckmanOpdam polynomials of type An with geometric parameter. For k=1 we obtain the most complete results. In this case we give an explicit expression of the matrix weight, which we show to be irreducible whenever n≥2. We also give explicit expressions of the spherical functions that determine the matrix weight for k=1. These expressions are used to calculate the spherical functions that determine the matrix weight for general k up to invertible uppertriangular matrices. This generalizes and gives a new proof of a formula originally obtained by Koornwinder for the case n=1. The commuting family of differential operators that have the matrixvalued polynomials as simultaneous eigenfunctions contains an element of order one. We give explicit formulas for differential operators of order one and two for (n,k) equal to (2,1) and (3,1).

Existence of diametrically complete sets with empty interior in reflexive and separable Banach spaces J. Funct. Anal. (IF 1.637) Pub Date : 20191127
Monika Budzyńska; Tadeusz Kuczumow; Simeon Reich; Mariola WalczykIn this paper we prove that every infinitedimensional and separable Banach space (X,‖⋅‖X) admits an equivalent norm ‖⋅‖X,1 such that (X,‖⋅‖X,1) has both the KadecKlee and the Opial properties. This result also has a quantitative aspect and when combined with the properties of Schauder bases and the Day norm it constitutes a basic tool in the proof of our main theorem: each infinitedimensional, reflexive and separable Banach space (X,‖⋅‖X) has an equivalent norm ‖⋅‖0 such that (X,‖⋅‖0) is LUR and contains a diametrically complete set with empty interior.

Decay estimates for a dissipativedispersive linear semigroup and application to the viscous Boussinesq equation J. Funct. Anal. (IF 1.637) Pub Date : 20191127
Guowei Liu; Weike WangAt the core of this article is the new estimate for a class of dissipativedispersive linear semigroup eΔt±ip(∇)t arising in the study of the viscous Boussinesq equation. We combine the decay estimate with introducing a set of timeweighted Sobolev spaces, where the timeweights and the regularity of the Sobolev spaces are determined by our decay estimate, to show the global existence and asymptotic behavior of solutions to the viscous Boussinesq equation in Rn.

Higher order Sobolev trace inequalities on balls revisited J. Funct. Anal. (IF 1.637) Pub Date : 20191127
Quốc Anh Ngô; Van Hoang Nguyen; Quoc Hung PhanInspired by a recent sharp Sobolev trace inequality of order four on the balls Bn+1 found by Ache and Chang (2017) [2], we propose a different approach to reprove Ache–Chang's trace inequality. To further illustrate this approach, we reprove the classical Sobolev trace inequality of order two on Bn+1 and provide sharp Sobolev trace inequalities of orders six and eight on Bn+1. To obtain all these inequalities up to order eight, and possibly more, we first establish higher order sharp Sobolev trace inequalities on R+n+1, then directly transferring them to the ball via a conformal change. As the limiting case of the Sobolev trace inequalities, Lebedev–Milin type inequalities of order up to eight are also considered.

Regular propagators of bilinear quantum systems J. Funct. Anal. (IF 1.637) Pub Date : 20191127
Nabile Boussaïd; Marco Caponigro; Thomas ChambrionThe present analysis deals with the regularity of solutions of bilinear control systems of the type x′=(A+u(t)B)x where the state x belongs to some complex infinite dimensional Hilbert space, the (possibly unbounded) linear operators A and B are skewadjoint and the control u is a real valued function. Such systems arise, for instance, in quantum control with the bilinear Schrödinger equation. For the sake of the regularity analysis, we consider a more general framework where A and B are generators of contraction semigroups. Under some hypotheses on the commutator of the operators A and B, it is possible to extend the definition of solution for controls in the set of Radon measures to obtain precise a priori energy estimates on the solutions, leading to a natural extension of the celebrated noncontrollability result of Ball, Marsden, and Slemrod in 1982.

The Steklov and Laplacian spectra of Riemannian manifolds with boundary J. Funct. Anal. (IF 1.637) Pub Date : 20191127
Bruno Colbois; Alexandre Girouard; Asma HassannezhadGiven two compact Riemannian manifolds M1 and M2 such that their respective boundaries Σ1 and Σ2 admit neighbourhoods Ω1 and Ω2 which are isometric, we prove the existence of a constant C such that σk(M1)−σk(M2)≤C for each k∈N. The constant C depends only on the geometry of Ω1≅Ω2. This follows from a quantitative relationship between the Steklov eigenvalues σk of a compact Riemannian manifold M and the eigenvalues λk of the Laplacian on its boundary. Our main result states that the difference σk−λk is bounded above by a constant which depends on the geometry of M only in a neighbourhood of its boundary. The proofs are based on a Pohozaev identity and on comparison geometry for principal curvatures of parallel hypersurfaces. In several situations, the constant C is given explicitly in terms of bounds on the geometry of Ω1≅Ω2.

Tensor algebras of product systems and their C⁎envelopes J. Funct. Anal. (IF 1.637) Pub Date : 20191127
Adam DorOn; Elias KatsoulisLet (G,P) be an abelian, lattice ordered group and let X be a compactly aligned product system over P with coefficients in A. We show that the C*envelope of the Nica tensor algebra NTX+ coincides with both Sehnem's covariance algebra A×XP and the couniversal C⁎algebra NOXr for injective, gaugecompatible, Nicacovariant representations of Carlsen, Larsen, Sims and Vittadello. We give several applications of this result on both the selfadjoint and nonselfadjoint operator algebra theory. First we guarantee the existence of NOXr, thus settling a problem of Carlsen, Larsen, Sims and Vittadello which was open even for abelian, lattice ordered groups. As a second application, we resolve a problem posed by Skalski and Zacharias on dilating isometric representations of product systems to unitary representations. As a third application we characterize the C⁎envelope of the tensor algebra of a finitely aligned higherrank graph which also holds for topological higherrank graphs. As a final application we prove reduced HaoNg isomorphisms for generalized gauge actions of discrete groups on C⁎algebras of product systems. This generalizes recent results that were obtained by various authors in the case where (G,P)=(Z,N).

Perturbations of Gibbs semigroups and the nonselfadjoint harmonic oscillator J. Funct. Anal. (IF 1.637) Pub Date : 20191127
Lyonell BoultonLet T be the generator of a C0semigroup e−Tt which is of trace class for all t>0 (a Gibbs semigroup). Let A be another closed operator, Tbounded with Tbound equal to zero. In general T+A might not be the generator of a Gibbs semigroup. In the first half of this paper we give sufficient conditions on A so that T+A is the generator of a Gibbs semigroup. We determine these conditions in terms of the convergence of the DysonPhillips expansion in suitable Schattenvon Neumann norms. In the second half of the paper we consider T=Hϑ=−e−iϑ∂x2+eiϑx2, the nonselfadjoint harmonic oscillator, on L2(R) and A=V, a locally integrable potential growing like xα at infinity for 0≤α<2. We establish that the DysonPhillips expansion converges in r Schattenvon Neumann norm in this case for r large enough and show that Hϑ+V is the generator of a Gibbs semigroup e−(Hϑ+V)τ for argτ≤π2−ϑ≠π2. From this we determine high energy asymptotics for the eigenvalues and the resolvent norm of Hϑ+V.

Meromorphy of local zeta functions in smooth model cases J. Funct. Anal. (IF 1.637) Pub Date : 20191126
Joe Kamimoto; Toshihiro NoseIt is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the whole complex plane. But, in the case of general (C∞) smooth functions, the meromorphic extension problem is not obvious. Indeed, it has been recently shown that there exist specific smooth functions whose local zeta functions have singularities different from poles. In order to understand the situation of the meromorphic extension in the smooth case, we investigate a simple but essentially important case, in which the respective function is expressed as u(x,y)xayb+ flat function, where u(0,0)≠0 and a,b are nonnegative integers. After classifying flat functions into four types, we precisely investigate the meromorphic extension of local zeta functions in each case. Our results show new interesting phenomena in one of these cases. Actually, when a−1/a and their poles on the halfplane are contained in the set {−k/b:k∈Nwithk

A Wiener test à la Landis for evolutive Hörmander operators J. Funct. Anal. (IF 1.637) Pub Date : 20191126
Giulio Tralli; Francesco UguzzoniIn this paper we prove a Wienertype characterization of boundary regularity, in the spirit of a classical result by Landis, for a class of evolutive Hörmander operators. We actually show the validity of our criterion for a larger class of degenerateparabolic operators with a fundamental solution satisfying suitable twosided Gaussian bounds. Our condition is expressed in terms of a series of balayages or, (as it turns out to be) equivalently, Rieszpotentials.

Geometry of C⁎algebras, and the bidual of their projective tensor product J. Funct. Anal. (IF 1.637) Pub Date : 20191125
Matthias NeufangGiven C⁎algebras A and B, consider the Banach algebra A⊗γB, where ⊗γ denotes the projective Banach space tensor product. If A and B are commutative, this is the Varopoulos algebra VA,B; we write VA for VA,A. It has been an open problem for almost 40 years to determine precisely when A⊗γB is Arens regular; see, e.g., [33], [48], [49]. Even the commutative situation, in particular the case A=B=ℓ∞, has remained unsolved. We solve this classical question for arbitrary C⁎algebras. Indeed, we show that A⊗γB is Arens regular if and only if A or B has the Phillips property; note that A has the latter property if and only if it is scattered and has the Dunford–Pettis Property. A further equivalent condition is that A⁎ has the Schur property, or, again equivalently, the enveloping von Neumann algebra A⁎⁎ is finite atomic, i.e., a direct sum of matrix algebras. Hence, Arens regularity of A⊗γB is entirely encoded in the geometry of the C⁎algebras. In case A and B are von Neumann algebra, we conclude that A⊗γB is Arens regular (if and) only if A or B is finitedimensional. We also show that this characterization does not generalize to the class of nonselfadjoint dual (even commutative) operator algebras. Specializing to commutative C⁎algebras A and B, we obtain that VA,B is Arens regular if and only if A or B is scattered. We further describe the centre Z(VA⁎⁎), showing that it is Banach algebra isomorphic to A⁎⁎⊗ehA⁎⁎, where ⊗eh denotes the extended Haagerup tensor product. We deduce that VA is strongly Arens irregular (if and) only if A is finitedimensional. Hence, VA is neither Arens regular nor strongly Arens irregular, if and only if A is nonscattered; as mentioned above, this is new even for the case A=ℓ∞.

Amenability of Beurling algebras, corrigendum to a result in “Generalised notions of amenability, II” [J. Funct. Anal. 254 (7) (2008) 1776–1810] J. Funct. Anal. (IF 1.637) Pub Date : 20191120
Fereidoun Ghahramani; Richard J. Loy; Yong ZhangWe fix a gap in the proof of a result in our earlier paper “Generalised notions of amenability, II” (F. Ghahramani et al. (2008) [2]), and so provide a new proof to a characterization of amenability for Beurling algebras. The result answers a question raised by M.C. White (1991) [6].

Gradient estimates for heat kernels and harmonic functions J. Funct. Anal. (IF 1.637) Pub Date : 20191113
Thierry Coulhon; Renjin Jiang; Pekka Koskela; Adam SikoraLet (X,d,μ) be a doubling metric measure space endowed with a Dirichlet form E deriving from a “carré du champ”. Assume that (X,d,μ,E) supports a scaleinvariant L2Poincaré inequality. In this article, we study the following properties of harmonic functions, heat kernels and Riesz transforms for p∈(2,∞]: (i) (Gp): Lpestimate for the gradient of the associated heat semigroup; (ii) (RHp): Lpreverse Hölder inequality for the gradients of harmonic functions; (iii) (Rp): Lpboundedness of the Riesz transform (p<∞); (iv) (GBE): a generalised BakryÉmery condition. We show that, for p∈(2,∞), (i), (ii) (iii) are equivalent, while for p=∞, (i), (ii), (iv) are equivalent. Moreover, some of these equivalences still hold under weaker conditions than the L2Poincaré inequality. Our result gives a characterisation of LiYau's gradient estimate of heat kernels for p=∞, while for p∈(2,∞) it is a substantial improvement as well as a generalisation of earlier results by AuscherCoulhonDuongHofmann [7] and AuscherCoulhon [6]. Applications to isoperimetric inequalities and Sobolev inequalities are given. Our results apply to Riemannian and subRiemannian manifolds as well as to nonsmooth spaces, and to degenerate elliptic/parabolic equations in these settings.
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