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  • Remarks on Painlevé’s differential equation P 34
    J. Anal. Math. (IF 0.949) Pub Date : 2020-11-12
    Norbert Steinmetz

    This paper is engaged with Painlevé’s differential equation P34:2ww″ = w″2 + 2w2(2w − z) − α, also known as Ince’s equation XXXIV and closely related to Painlevé’s second differential equation \({{\rm{P}}_\Pi}:\varpi\prime\prime= \alpha + z\varpi + 2{\varpi^3}\). We will show that the transcendental solutions belong to the Yosida class \({\mathfrak{Y}_{{\rm{1,}}{1 \over 2}}}\) and have no deficient

  • Continuity of the flow map for symmetric hyperbolic systems and its application to the Euler-Poisson system
    J. Anal. Math. (IF 0.949) Pub Date : 2020-11-12
    Uwe Brauer, Lavi Karp

    We show the continuity of the flow map for quasilinear symmetric hyperbolic systems with general right-hand sides in different functional setting, including weighted Sobolev spaces Hs δ. An essential tool to achieve the continuity of the flow map is a new type of energy estimate, which we call a low regularity energy estimate. We then apply these results to the Euler-Poisson system which describes

  • Asymptotics of Chebyshev Polynomials. IV. Comments on the Complex Case
    J. Anal. Math. (IF 0.949) Pub Date : 2020-11-12
    Jacob S. Christiansen, Barry Simon, Maxim Zinchenko

    We make a number of comments on Chebyshev polynomials for general compact subsets of the complex plane. We focus on two aspects: asymptotics of the zeros and explicit Totik–Widom upper bounds on their norms.

  • Speiser class Julia sets with dimension near one
    J. Anal. Math. (IF 0.949) Pub Date : 2020-11-12
    Simon Albrecht, Christopher J. Bishop

    for any δ > 0 we construct an entire function f with three singular values whose Julia set has Hausdorff dimension at most 1 + δ. Stallard proved that the dimension must be strictly larger than 1 whenever f has a bounded singular set, but no examples with finite singular set and dimension strictly less than 2 were previously known.

  • Radially distributed values and normal families. II
    J. Anal. Math. (IF 0.949) Pub Date : 2020-11-12
    Walter Bergweiler, Alexandre Eremenko

    We consider the family of all functions holomorphic in the unit disk for which the zeros lie on one ray while the 1-points lie on two different rays. We prove that for certain configurations of the rays this family is normal outside the origin.

  • On the bounded cohomology of ergodic group actions
    J. Anal. Math. (IF 0.949) Pub Date : 2020-11-12
    Jon Aaronson, Benjamin Weiss

    In this note we show existence of bounded, continuous, transitive cocycles over a transitive action by homeomorphisms of any finitely generated group on a Polish space, and bounded, measurable, ergodic cocycles over any ergodic, probability-preserving action of ℤd.

  • Non p -norm approximated Groups
    J. Anal. Math. (IF 0.949) Pub Date : 2020-11-12
    Alexander Lubotzky, Izhar Oppenheim

    It was shown in a previous work of the first-named author with De Chiffre, Glebsky and Thom that there exists a finitely presented group which cannot be approximated by almost-homomorphisms to the unitary groups U(n) equipped with the Frobenius norms (a.k.a. as L2 norm, or the Schatten-2-norm). In his ICM18 lecture, Andreas Thom asks if this result can be extended to general Schatten-p-norms. We show

  • Transversality in the setting of hyperbolic and parabolic maps
    J. Anal. Math. (IF 0.949) Pub Date : 2020-11-12
    Genadi Levin, Weixiao Shen, Sebastian van Strien

    In this paper we consider families of holomorphic maps defined on subsets of the complex plane, and show that the technique developed in [24] to treat unfolding of critical relations can also be used to deal with cases where the critical orbit converges to a hyperbolic attracting or a parabolic periodic orbit. As before this result applies to rather general families of maps, such as polynomial-like

  • Universality and distribution of zeros and poles of some zeta functions
    J. Anal. Math. (IF 0.949) Pub Date : 2020-11-12
    Kristian Seip

    This paper studies zeta functions of the form \(\sum\nolimits_{n = 1}^\infty {\chi (n){n^{- s}}}\), with χ a completely multiplicative function taking only unimodular values. We denote by σ(χ) the infimum of those α such that the Dirichlet series \(\sum\nolimits_{n = 1}^\infty {\chi (n){n^{- s}}}\) can be continued meromorphically to the half-plane Re s > α, and denote by ζχ(s) the corresponding meromorphic

  • Local asymptotics for orthonormal polynomials on the unit circle via universality
    J. Anal. Math. (IF 0.949) Pub Date : 2020-11-12
    Doron S. Lubinsky

    Let µ be a positive measure on the unit circle that is regular in the sense of Stahl, Totik, and Ullmann. Assume that in some subarc J, µ is absolutely continuous, while µ′ is positive and continuous. Let {φn} be the orthonormal polynomials for µ. We show that for appropriate ζn ∈ J, \({{\rm{\{ }}{{{\varphi _n}({\zeta _n}(1 + {\textstyle{z \over n}}))} \over {{\varphi _n}({\zeta _n})}}{\rm{\}}}_{n

  • Free boundary minimal surfaces and overdetermined boundary value problems
    J. Anal. Math. (IF 0.949) Pub Date : 2020-11-12
    Nikolai S. Nadirashvili, Alexei V. Penskoi

    In this paper we establish a connection between free boundary minimal surfaces in a ball in ℝ3 and free boundary cones arising in a one-phase problem.

  • Domains of unicity
    J. Anal. Math. (IF 0.949) Pub Date : 2020-11-12
    Vilmos Totik

    The Gale–Nikaido theorem claims that if the Jacobian of a mapping F is a P-matrix at every point of K and K is a closed rectangular region in Rn, then F is globally univalent on K. Under the more severe condition that the (symmetric part of the) Jacobian is positive definite on K, the same conclusion is valid on any closed convex set K. In this paper it is shown that the closed rectangular regions

  • Locally polynomially integrable surfaces and finite stationary phase expansions
    J. Anal. Math. (IF 0.949) Pub Date : 2020-11-12
    Mark Agranovsky

    Let M be a strictly convex smooth connected hypersurface in ℝn and \(\widehat{M}\) its convex hull. We say that M is locally polynomially integrable if for every point a ∈ M the (n − 1)-dimensional volume of the cross-section of \(\widehat{M}\) by a parallel translation of the tangent hyperplane at a to a small distance t depends polynomially on t. It is conjectured that only quadrics in odd-dimensional

  • A spectral cocycle for substitution systems and translation flows
    J. Anal. Math. (IF 0.949) Pub Date : 2020-11-12
    Alexander I. Bufetov, Boris Solomyak

    for substitution systems and translation flows, a new cocycle, which we call the spectral cocycle, is introduced, whose Lyapunov exponents govern the local dimension of the spectral measure for higher-level cylindrical functions. The construction relies on the symbolic representation of translation flows and the formalism of matrix Riesz products.

  • Bank–Laine functions, the Liouville transformation and the Eremenko–Lyubich class
    J. Anal. Math. (IF 0.949) Pub Date : 2020-11-12
    James K. Langley

    The Bank–Laine conjecture concerning the oscillation of solutions of second order homogeneous linear differential equations has recently been disproved by Bergweiler and Eremenko. It is shown here, however, that the conjecture is true if the set of finite critical and asymptotic values of the coefficient function is bounded. It is also shown that if E is a Bank–Laine function of finite order with infinitely

  • Direct Cauchy theorem and Fourier integral in Widom domains
    J. Anal. Math. (IF 0.949) Pub Date : 2020-11-12
    Peter Yuditskii

    We derive the Fourier integral associated with the complex Martin function in the Denjoy domain of the Widom type with the Direct Cauchy Theorem (DCT). As an application we study canonical systems and corresponding transfer matrices generated by reflectionless Weyl-Titchmarsh functions in such domains. The DCT property appears to be crucial in many aspects of the underlying theory.

  • On the hyperbolic distance of n -times punctured spheres
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Toshiyuki Sugawa, Matti Vuorinen, Tanran Zhang

    The shortest closed geodesic in a hyperbolic surface X is called a systole of X. When X is an n-times punctured sphere \(\mathbb{C}\widehat\backslash A\) where \(A \subset \widehat {\mathbb{C}}\) is a finite set of cardinality n ≥ 4, we define a quantity Q(A) in terms of cross ratios of quadruples in A so that Q(A) is quantitatively comparable with the systole length of X. We next propose a method

  • Central limit theorems for group actions which are exponentially mixing of all orders
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Michael Björklund, Alexander Gorodnik

    In this paper we establish a general dynamical Central Limit Theorem (CLT) for group actions which are exponentially mixing of all orders. In particular, the main result applies to Cartan flows on finite-volume quotients of simple Lie groups. Our proof uses a novel relativization of the classical method of cumulants, which should be of independent interest. As a sample application of our techniques

  • Improved estimates for polynomial Roth type theorems in finite fields
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Dong Dong, Xiaochun Li, Will Sawin

    We prove that, under certain conditions on the function pair ϕ1 and ϕ2, the bilinear average \({q^{- 1}}\sum\nolimits_{y \in {\mathbb{F}_q}} {{f_1}\left({x + {\varphi _2}\left(y \right)} \right){f_2}\left({x + {\varphi _2}\left(y \right)} \right)} \) along the curve (ϕ1, ϕ2) satisfies a certain decay estimate. As a consequence, Roth type theorems hold in the setting of finite fields. In particular

  • Blow-up profiles and life beyond blow-up in the fully parabolic Keller-Segel system
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Michael Winkler

    The fully parabolic Keller-Segel system is considered in n-dimensional balls with n ≥ 2. Pointwise time-independent estimates are derived for arbitrary radially symmetric solutions. These are firstly used to assert that any radial classical solution which blows up in finite time possesses a uniquely determined blow-up profile which satisfies an associated pointwise upper inequality. Secondly, in conjunction

  • Feynman path integrals for magnetic Schrödinger operators on infinite weighted graphs
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Batu Güneysu, Matthias Keller

    We prove a Feynman path integral formula for the unitary group exp(—itLυ,θ), t ≥ 0, associated with a discrete magnetic Schrödinger operator Lυ,θ on a large class of weighted infinite graphs. As a consequence, we get a new Kato-Simon estimate \(\left| {\exp \left({- it{L_{v,\theta}}} \right)\left({x,y} \right)} \right| \le \exp \left({- t{L_{- \deg ,0}}} \right)\left({x,y} \right),\) which controls

  • Strongly automorphic mappings and Julia sets of uniformly quasiregular mappings
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Alastair Fletcher, Douglas Macclure

    A theorem of Ritt states the Poincaré linearizer L of a rational map f at a repelling fixed point is periodic only if f is conjugate to a power of z, a Chebyshev polynomial or a Lattes map. The converse, except for the case where the fixed pointis an endpoint of the interval Julia set for a Chebyshev polynomial, is also true. In this paper, we prove the analogous statement in the setting of strongly

  • Planck-scale distribution of nodal length of arithmetic random waves
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Jacques Benatar, Domenico Marinucci, Igor Wigman

    We study the nodal length of random toral Laplace eigenfunctions (“arithmetic random waves”) restricted to decreasing domains (“shrinking balls”), all the way down to Planck scale. We find that, up to a natural scaling, for “generic” energies the variance of the restricted nodal length obeys the same asymptotic law as the total nodal length, and these are asymptotically fully correlated. This, among

  • Extreme points in the isometric embedding problem for model spaces
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Leonid Golinskii

    In 1996 A. Aleksandrov solved the isometric embedding problem for the model spaces KΘ with an arbitrary inner function Θ.We find all extreme points of this convex set of measures in the case when & is a finite Blaschke product, and obtain some partial results for generic inner functions.

  • Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Wencai Liu, Darren C. Ong

    In this paper, we consider the Schrödinger equation, \(Hu = - {u^"} + \left({V\left(x \right) + {V_0}\left(x \right)} \right)u = Eu,\) where V0(x) is 1-periodic and V(x) is a decaying perturbation. By Floquet theory, the spectrum of H0 = − ∇2 + V0 is purely absolutely continuous and consists of a union of closed intervals (often referred to as spectral bands). Given any finite set of points \(\left\{{{E_j}}

  • A smooth zero-entropy diffeomorphism whose product with itself is loosely Bernoulli
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Marlies Gerber, Philipp Kunde

    Let M be a smooth compact connected manifold of dimension d ≥ 2, possibly with boundary, that admits a smooth effective \({\mathbb{T}^2}\)-action \({\cal S} = {\left\{{{S_{\alpha ,\beta}}} \right\}_{\left({\alpha ,\beta} \right) \in {\mathbb{T}^2}}}\) preserving a smooth volume v, and let \({\cal B}\) be the C∞ closure of \(\left\{{h\, \circ {S_{\alpha ,\beta}} \circ {h^{- 1}}:h \in {\rm{Dif}}{{\r

  • Sharp regularity for the inhomogeneous porous medium equation
    J. Anal. Math. (IF 0.949) Pub Date : 2020-03-25
    Damião J. Araújo, Anderson F. Maia, José Miguel Urbano

    We show that locally bounded solutions of the inhomogeneous porous medium equation $$u_{t}-\operatorname{div}\left(m|u|^{m-1} \nabla u\right)=f \in L^{q, r}, \quad m>1$$ are locally Hölder continuous, with exponent $$\gamma = \min \{ {{\alpha _0^ - } \over m},\;{{[(2q - n)r - 2q]} \over {q[(mr - (m - 1)]}}\} ,$$ where α0 denotes the optimal Hölder exponent for solutions of the homogeneous case. The

  • Cesàro bounded operators in Banach spaces
    J. Anal. Math. (IF 0.949) Pub Date : 2020-03-25
    Teresa Bermúdez, Antonio Bonilla, Vladimír Müller, Alfredo Peris

    We study several notions of boundedness for operators. It is known that any power bounded operator is absolutely Cesàro bounded and strongly Kreiss bounded (in particular, uniformly Kreiss bounded). The converses do not hold in general. In this note, we give examples of topologically mixing (hence, not power bounded) absolutely Cesàro bounded operators on ℓp(ℕ), 1 ≤ p < ∞, and provide examples of uniformly

  • A Schwarz lemma at the boundary on complex Hilbert balls and applications to starlike mappings
    J. Anal. Math. (IF 0.949) Pub Date : 2020-03-23
    Ian Graham, Hidetaka Hamada, Gabriela Kohr

    In this paper, we prove a Schwarz lemma at the boundary for holomorphic mappings f between Hilbert balls, and obtain related consequences. Especially, we obtain estimations of ∥Df(z0)∥ on the holomorphic tangent space for holomorphic mappings f or for homogeneous polynomial mappings f between Hilbert balls. Next, we prove the boundary rigidity theorem for holomorphic self-mappings of a Hilbert ball

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