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WoldType Decompositions for Pairs of Commutative Semigroups Generated by Isometries Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220729
T. Bînzar, C. LăzureanuAbstract In this paper we analyze connections between Woldtype decompositions of bi/isometries and pairs of semigroups of isometries, where at least one of semigroups is a product semigroup generated by two isometries.

On the Milnor and Tjurina Numbers of ZeroDimensional Singularities Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220729
A. G. AleksandrovAbstract In this paper we study relationships between some topological and analytic invariants of zerodimensional germs, or multiple points. Among other things, it is shown that there exist no rigid zerodimensional Gorenstein singularities and rigid almost complete intersections. In the proof of the first result we exploit the canonical duality between homology and cohomology of the cotangent complex

Strengthening of the Bourgain–Kontorovich Theorem on Small Values of Hausdorff Dimension Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220729
I. D. KanAbstract Let \(\mathfrak{D}_\mathbf{A}(N)\) be the set of all integers not exceeding \(N\) and equal to irreducible denominators of positive rational numbers with finite continued fraction expansions in which all partial quotients belong to a finite number alphabet \(\mathbf{A}\). A new lower bound for the cardinality \(\mathfrak{D}_\mathbf{A}(N)\) is obtained, whose nontrivial part improves that

TwoSided Estimates of the $$K$$ Functional for Spaces of Functions of Generalized Bounded Variation Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220729
E. I. BerezhnoiAbstract A twosided estimate is proposed for the \(K\)functional of the pair \((C[0,1], BV(X))\), where \(BV(X)\) is the space of functions of generalized bounded variation constructed from a symmetric sequence space \(X\). The application of this estimate to various sequence spaces \(X\) yields new interpolation theorems for spaces of finite Wiener–Young \(h\)variation, of finite Waterman \(\Lambda\)variation

Polynomials in the Differentiation Operator and Formulas for the Sums of Certain Convergent Series Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220729
K. A. Mirzoev, T. A. SafonovaAbstract Let \(P_n(x)\) be any polynomial of degree \(n\geq 2\) with real coefficients such that \(P_n(k)\ne 0\) for \(k\in\mathbb{Z}\). In the paper, in particular, the sum of a series of the form \(\sum_{k=\infty}^{+\infty}1/P_n(k)\) is expressed as the value at \((0,0)\) of the Green function of the selfadjoint problem generated by the differential expression \(l_n[y]=P_n(i\,d/dx) y\) and the

A Hilbert $$C^*$$ Module with Extremal Properties Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220729
D. V. FufaevAbstract We construct an example of a Hilbert \(C^*\)module which shows that Troitsky’s theorem on the geometric essence of \( {\mathcal A} \)compact operators between Hilbert \(C^*\)modules cannot be extended to modules which are not countably generated case (even in the case of a stronger uniform structure, which is also introduced). In addition, the constructed module admits no frames.

On a Notion of Averaged Mappings in $$\operatorname{CAT}(0)$$ Spaces Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220729
A. BërdëllimaAbstract We introduce a notion of averaged mappings in the broader class of \(\operatorname{CAT}(0)\) spaces. We call these mappings \(\alpha\)firmly nonexpansive and develop basic calculus rules for ones that are quasi\(\alpha\)firmly nonexpansive and have a common fixed point. We show that the iterates \(x_n:=Tx_{n1}\) of a nonexpansive mapping \(T\) converge weakly to an element in \(\operatorname{Fix}

Resonances for the Dirac Operator on the HalfLine Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220317
E. L. Korotyaev, D. S. MokeevAbstract We consider the inverse problem for a massless Dirac operator on the halfline such that the support of its potential has fixed upper boundary and solve it in terms of a Jost function and a scattering matrix. We prove that the potential of such an operator is uniquely determined by its resonances.

Note on Derivations of Certain nonCSL Algebras Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220317
Chaoqun Chen, Fangyan LuAbstract A subspace lattice \(\{(0), M, N, H\}\) of a Hilbert space \(H\) is called a generalized generic lattice if \(M\cap N =M^\perp\cap N^\perp =(0)\) and \(\dim (M^\perp \cap N)=\dim (M\cap N^\perp)\). In this note, we show that each derivation of a generalized generic lattice algebra into itself is inner.

Dunkl Translations, DunklType BMO Space, and Riesz Transforms for the Dunkl Transform on $$L^\infty$$ Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220317
Wentao TengAbstract In this paper we will give some results on the support of Dunkl translations on compactly supported functions. Then we will define the Dunkltype BMO space and Riesz transforms for the Dunkl transform on \(L^\infty\) and prove the boundedness of the Riesz transforms from \(L^\infty\) to the Dunkltype BMO space under the assumption of the uniform boundedness of Dunkl translations. The proof

Infinitesimal Center Problem on Zero Cycles and the Composition Conjecture Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220317
A. Álvarez, J. L. Bravo, C. Christopher, P. MardešićAbstract We study the analog of the classical infinitesimal center problem in the plane, but for zero cycles. We define the displacement function in this context and prove that it is identically zero if and only if the deformation has a composition factor. That is, we prove that here the composition conjecture is true, in contrast with the tangential center problem on zero cycles. Finally, we give

SingleValued Extension Property and Property $$(\omega)$$ Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220317
Lili Yang, Xiaohong CaoAbstract We study the stability of the singlevalued extension property for operators on a Hilbert space. Further, relations between the stability of the singlevalued extension property and of property \((\omega)\) are given.

Localization for Hyperbolic Measures on InfiniteDimensional Spaces Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220317
A. N. KalininAbstract Properties of the extreme points of families of concave measures on infinitedimensional locally convex spaces are studied. The localization method is generalized to hyperbolic measures on Fréchet spaces.

A Note on Relatively Injective $$C_0(S)$$ Modules $$C_0(S)$$ Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220317
N. T. NemeshAbstract In this note we discuss some necessary and some sufficient conditions for the relative injectivity of the \(C_0(S)\)module \(C_0(S)\), where \(S\) is a locally compact Hausdorff space. We also give a Banach module version of Sobczyk’s theorem. The main result of the paper is as follows: if the \(C_0(S)\)module \(C_0(S)\) is relatively injective, then \(S=\beta(S\setminus \{s\})\) for any

The BiHamiltonian Structures of the DR and DZ Hierarchies in the Approximation up to Genus One Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220317
O. Brauer, A. Yu. BuryakAbstract In a recent paper, given an arbitrary homogeneous cohomological field theory ( CohFT), Rossi, Shadrin, and the first author proposed a simple formula for a bracket on the space of local functionals, which conjecturally gives a second Hamiltonian structure for the double ramification hierarchy associated to the CohFT. In this paper we prove this conjecture in the approximation up to genus \(1\)

On Rduals of Type III in Hilbert Spaces Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220125
H. Führ, J. Cheshmavar, A. AkbarniaAbstract Following work by Casazza, Kutyniok, and Lammers and its development by Stoeva and Christensen, we provide some novel characterizations of Rdual sequences of type III in Hilbert spaces. We systematically extend the construction procedure by basing it on a choice of an antiunitary involution. For certain classes of Rduals of type III, we derive a representation of the associated frame operator

Hyperelliptic Sigma Functions and Adler–Moser Polynomials Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220125
V. M. Buchstaber, E. Yu. BunkovaAbstract In a 2004 paper by V. M. Buchstaber and D. V. Leykin, published in “Functional Analysis and Its Applications,” for each \(g > 0\), a system of \(2g\) multidimensional heat equations in a nonholonomic frame was constructed. The sigma function of the universal hyperelliptic curve of genus \(g\) is a solution of this system. In our previous work, published in “Functional Analysis and Its Applications

The Schur–Weyl Graph and Thoma’s Theorem Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220125
A. M. Vershik, N. V. TsilevichAbstract We define a graded graph, called the Schur–Weyl graph, which arises naturally when one considers simultaneously the RSK algorithm and the classical duality between representations of the symmetric and general linear groups. As one of the first applications of this graph, we give a new proof of the completeness of the list of discrete indecomposable characters of the infinite symmetric group

On the Set of Continuity of the Topological Entropy of ParameterDependent Mappings of the Interval Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220125
A. N. VetokhinAbstract Families of continuous mappings of the interval continuously depending on a parameter are considered. Any \(G_\delta\) set dense in the parameter space is realized as the set of continuity of topological entropy for a suitable family of continuous mappings.

Connection on the Group of Diffeomorphisms as a Bundle Over the Space of Functions Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220125
S. M. GuseinZadeAbstract Jacobian determines a bundle with total space consisting of orientationpreserving diffeomorphisms of a (connected) manifold over the space of positive functions on this manifold (with integral equal to volume for a compact manifold). It is proved that, for the \(n\)sphere with standard metric, there is a unique connection on this bundle that is invariant with respect to all isometries of

Dirac Operators with Singular Potentials Supported on Unbounded Surfaces in $$\mathbb{R}^{3}$$ Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220125
V. S. RabinovichAbstract We consider the selfadjointness and essential spectrum of 3D Dirac operators with bounded variable magnetic and electrostatic potentials and with singular deltatype potentials with supports on uniformly regular unbounded surfaces \(\Sigma\) in \(\mathbb{R}^{3}\).

Maximal Monotonicity of a Nemytskii Operator Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220125
A. A. TolstonogovAbstract A family of maximally monotone operators on a separable Hilbert space is considered. The domains of these operators depend on time ranging over an interval of the real line. The space of squareintegrable functions on this interval taking values in the same Hilbert space is also considered. On the space of squareintegrable functions a superposition (Nemytskii) operator is constructed based

Rational Hypergeometric Identities Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220125
G. A. Sarkissian, V. P. SpiridonovAbstract A special singular limit \(\omega_1/\omega_2 \to 1\) is considered for the Faddeev modular quantum dilogarithm (hyperbolic gamma function) and the corresponding hyperbolic integrals. It brings a new class of hypergeometric identities associated with bilateral sums of Mellin–Barnes type integrals of particular Pochhammer symbol products.

On Approximation of Measures by Their FiniteDimensional Images Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20220125
V. I. BogachevAbstract We consider Borel measures on separable Banach spaces that are limits of their finitedimensional images in the weak topology. The class of Banach spaces on which all measures have this property is introduced. The specified property is proved for all measures from the closure in variation of the linear span of the set of measures absolutely continuous with respect to Gaussian measures. Connections

Two Consequences of Davies’ Hardy Inequality Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20211108
Frank, R. L., Larson, S.Abstract Davies’ version of the Hardy inequality gives a lower bound for the Dirichlet integral of a function vanishing on the boundary of a domain in terms of the integral of the squared function with a weight containing the averaged distance to the boundary. This inequality is applied to easily derive two classical results of spectral theory, E. Lieb’s inequality for the first eigenvalue of the Dirichlet

On the Spectrum of the OneParticle Density Matrix Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20211108
Sobolev, A. V.Abstract The oneparticle density matrix \(\gamma(x, y)\) is one of the key objects in quantummechanical approximation schemes. The selfadjoint operator \(\Gamma\) with kernel \(\gamma(x, y)\) is trace class, but no sharp results on the decay of its eigenvalues were previously known. The note presents the asymptotic formula \(\lambda_k \sim (Ak)^{8/3}\), \(A \ge 0\), as \(k\to\infty\) for the eigenvalues

Eigenvalue Asymptotics for Weighted Polyharmonic Operator with a Singular Measure in the Critical Case Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20211108
Rozenblum, G. V., Shargorodsky, E. M.Abstract We find that, in the critical case \(2l= {\mathbf N} \), the eigenvalues of the problem \(\lambda(\Delta)^{l}u=Pu\) with the singular measure \(P\) supported on a compact Lipschitz surface of an arbitrary dimension in \( {\mathbb R} ^{ {\mathbf N} }\) satisfy an asymptotic formula of the same order as in the case of an absolutely continuous measure.

On Rotational Waves of Limit Amplitude Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20211108
Kozlov, V. A., Lokharu, E. E.Abstract In this note we discuss some recent results on extreme steady waves under gravity. They include the existence and regularity theorems for highest waves on finite depth with and without vorticity. Furthermore, we state new results concerning the asymptotic behavior of surface profiles near stagnation points. In particular, we find that the wave profile of an extreme wave is concave near each

Hardy Inequality for Antisymmetric Functions Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20211108
HoffmannOstenhof, T., Laptev, A.Abstract We consider Hardy inequalities on antisymmetric functions. Such inequalities have substantially better constants. We show that they depend on the lowest degree of an antisymmetric harmonic polynomial. This allows us to obtain some Caffarelli–Kohn–Nirenbergtype inequalities that are useful for studying spectral properties of Schrödinger operators.

Inequalities of Rellich Type Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20211108
Edmunds, D. E., Evans, W. D., Lewis, R. T.Abstract Hardy inequalities have been important topics of research for a century, and in the past twenty years or so, there has been a deluge of important papers on various versions, including discrete and fractional forms and extensions to Rellich and higherorder inequalities. This paper is a brief survey of known fractional and nonfractional forms of the Rellich inequality together with some new

Estimates for Schur Multipliers and Double Operator Integrals—A Wavelet Approach Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20211108
McDonald, E., Scheckter, T. T., Sukochev, F. A.Abstract We discuss the work of Birman and Solomyak on the singular numbers of integral operators from the point of view of modern approximation theory, in particular, with the use of wavelet techniques. We are able to provide a simple proof of norm estimates for integral operators with kernel in \(B^{1/p1/2}_{p,p}(\mathbb R,L_2(\mathbb R))\). This recovers, extends, and sheds new light on a theorem

Universal Relations in Asymptotic Formulas for Orthogonal Polynomials Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20211108
Yafaev, D. R.Abstract Orthogonal polynomials \(P_{n}(\lambda)\) are oscillating functions of \(n\) as \(n\to\infty\) for \(\lambda\) in the absolutely continuous spectrum of the corresponding Jacobi operator \(J\). We show that, irrespective of any specific assumptions on the coefficients of the operator \(J\), the amplitude and phase factors in asymptotic formulas for \(P_{n}(\lambda)\) are linked by certain universal

Titchmarsh–Weyl Formula for the Spectral Density of a Class of Jacobi Matrices in the Critical Case Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20211108
Naboko, S. N., Simonov, S. A.Abstract We consider a class of Jacobi matrices with unbounded entries in the socalled critical (double root, Jordan block) case. We prove a formula which relates the spectral density of a matrix to the asymptotics of orthogonal polynomials associated with it.

Homogenization of Nonstationary Maxwell System with Constant Magnetic Permeability Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20211108
Dorodnyi, M. A., Suslina, T. A.Abstract We study a nonstationary Maxwell system in \(\mathbb{R}^3\) with dielectric permittivity \(\eta(\varepsilon^{1}{\mathbf x})\) and magnetic permeability \(\mu\). Here \(\eta(\mathbf{x})\) is a positive definite bounded symmetric \((3 \times 3)\)matrix valued function periodic with respect to some lattice and \(\mu\) is a constant positive \(3\times 3\) matrix. We obtain approximations for

On the Symmetrizations of $$\varepsilon$$ Isometries on Positive Cones of Continuous Function Spaces Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210908
Sun, LongfaAbstract Let \(K\) be a compact Hausdorff space, \(C(K)\) be the real Banach space of all continuous functions on \(K\) endowed with the supremum norm, and \(C(K)^+\) be the positive cone of \(C(K)\). A weak stability result for the symmetrization \(\Theta=(f(\,\boldsymbol\cdot\,)f(\;\boldsymbol\cdot\,)/2\) of a general \(\varepsilon\)isometry \(f\) from \(C(K)^+\cupC(K)^+\) to a Banach space \(Y\)

Polynomial Somos Sequences Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210908
Bykovskii, V. A., Romanov, M. A.Abstract Algebraic characteristics of the polynomial Somos\(k\) sequences for \(k=4, 5, 6, 7\) are calculated.

Ergodicity and Totality of Partitions Associated with the RSK Correspondence Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210908
Vershik, A. M., Tsilevich, N. V.Abstract The asymptotic properties of sequences of partitions (\(\sigma\)algebras) associated with the Robinson–Schensted–Knuth correspondence in spaces with Bernoulli measures are studied.

On Sharp Estimates of EvenOrder Derivatives in Sobolev Spaces Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210908
Garmanova, T. A., Sheipak, I. A.Abstract The norms of embedding operators \(\mathring{W}^n_2[0,1]\hookrightarrow\mathring{W}^k_\infty[0,1]\) (\(0\leqslant k\leqslant n1\)) of Sobolev spaces are considered. The least possible values of \(A^2_{n,k}(x)\) in the inequalities \(f^{(k)}(x)^2\leqslant A^2_{n,k}(x)\f^{(n)}\^2_{L_2[0,1]}\) (\(f\in \mathring{W}^n_2[0,1]\)) are studied. On the basis of relations between the functions \(A^2_{n

On Simple $${\mathbb Z}_3$$ Invariant Function Germs Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210908
GuseinZade, S. M., Rauch, A.M. Ya.Abstract V. I. Arnold classified simple (i.e., having no moduli for classification) singularities (function germs) and also simple boundary singularities, that is, function germs invariant with respect to the action \(\sigma(x_1; y_1,\dots, y_n)=(x_1; y_1,\dots, y_n)\) of the group \({\mathbb Z}_2\). In particular, he showed that a function germ (a germ of a boundary singularity) is simple if and

Interfacial Contact Model in a Dense Network of Elastic Materials Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210908
Abouelhanoune, Y., El Jarroudi, M.Abstract We consider a dense network of elastic materials modeled by a dense network of elastic disks. More specifically, we consider a dense network of elastic disks in the unit disk \(D(0,1)\) of \(\mathbb{R}^{2}\) obtained from an Apollonian packing of elastic circular disks by removing disks of small sizes. We suppose that the disks are pressed against each other to form small rectilinear contact

Multivariate Signatures of Iterated Torus Links Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210908
Orevkov, S. Yu.Abstract We compute the multivariate signatures of any Seifert link (that is, a union of some fibers in a Seifert homology sphere), in particular, of the union of a torus link with one or both of its cores (cored torus link). The signatures of cored torus links are used in the Degtyarev–Florens–Lecuona splicing formula for computing multivariate signatures of cables over links. We use Neumann’s computation

On Numerically Implementable Explicit Formulas for the Solutions to the 2D and 3D Equations $$\operatorname{div}(\alpha(w)\nabla w)=0$$ and $$\operatorname{div}(\beta\nabla w)=0$$ with Cauchy Data on an Analytic Boundary Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210908
Demidov, A. S.Abstract A construction of numerically implementable explicit expressions for the solutions of the two and threedimensional equations \(\operatorname{div}(\alpha(w)\nabla w)=0\) and \(\operatorname{div}(\beta\nabla w)=0\) with Cauchy data on an analytic boundary is presented.

On the Relative Projection Constants of Certain Classes of Subspaces of $$l_\infty^{2n}$$ Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210601
O. M. MartynovAbstract Relative projection constants of certain classes of cubspaces of codimension 2 in \(l_\infty^{2n}\) are found. The minimal projections under considerations are of two kinds, with unit norm and with norm larger than 1.

Generalized Trace Formula for Polynomials Orthogonal in ContinuousDiscrete Sobolev Spaces Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210601
B. P. OsilenkerAbstract In continuousdiscrete Sobolev spaces a generalized trace formula for orthogonal polynomials \(\{\widehat{q}_n\}_{n=0}^\infty\) is obtained. The proof of this formula is based on the representation of the Fejér kernel for the system \(\{\widehat{q}_n\}_{n=0}^\infty\). As a consequence, a generalized trace formula for Gegenbauer–Sobolev polynomials in a discrete Sobolev space is obtained.

Sigma Functions and Lie Algebras of Schrödinger Operators Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210601
V. M. Buchstaber, E. Yu. BunkovaAbstract In a 2004 paper by V. M. Buchstaber and D. V. Leikin, published in “Functional Analysis and Its Applications,” for each \(g > 0\), a system of \(2g\) multidimensional Schrödinger equations in magnetic fields with quadratic potentials was defined. Such systems are equivalent to systems of heat equations in a nonholonomic frame. It was proved that such a system determines the sigma function

Compact Operators and Uniform Structures in Hilbert $$C^*$$ Modules Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210601
E. V. Troitsky, D. V. FufaevAbstract Quite recently a criterion for the \(\mathcal{A}\)compactness of an ajointable operator \(F\colon {\mathcal M} \to\mathcal{N}\) between Hilbert \(C^*\)modules, where \(\mathcal{N}\) is countably generated, was obtained. Namely, a uniform structure (a system of pseudometrics) in \(\mathcal{N}\) was discovered such that \(F\) is \(\mathcal{A}\)compact if and only if \(F(B)\) is totally bounded

Expansive Endomorphisms on the InfiniteDimensional Torus Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210601
S. D. Glyzin, A. Yu. Kolesov, N. Kh. RozovAbstract A natural class of expansive endomorphisms \(G\in C^1\) of the infinitedimensional torus \(\mathbb{T}^{\infty}\) (the Cartesian product of countably many circles with the product topology) is considered. The endomorphisms in this class can be represented in the form of the sum of a linear expansion and a periodic addition. The following standard facts of hyperbolic theory are proved: the

On the Constancy of the Extremal Function in the Embedding Theorem of Fractional Order Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210601
N. S. UstinovAbstract We consider the problem of the constancy of the minimizer in the fractional embedding theorem \(\mathcal{H}^s(\Omega) \hookrightarrow L_q(\Omega)\) for a bounded Lipschitz domain \(\Omega\), depending on the domain size. For the family of domains \(\varepsilon \Omega\), we prove that, for small dilation coefficients \(\varepsilon\), the unique minimizer is constant, whereas for large \(\varepsilon\)

The Hermitian Jacobi Process: A Simplified Formula for the Moments and Application to Optical Fiber MIMO Channels Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210601
N. Demni, T. Hamdi, A. SouissiAbstract Using a change of basis in the algebra of symmetric functions, we compute the moments of the Hermitian Jacobi process. After a careful arrangement of terms and the evaluation of the determinant of an “almost uppertriangular” matrix, we end up with a moment formula which is considerably simpler than the one derived in [8]. As an application, we propose the Hermitian Jacobi process as a dynamical

Fourier Transform on the Lobachevsky Plane and Operational Calculus Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210601
Yu. A. NeretinAbstract The classical Fourier transform on the line sends the operator of multiplication by \(x\) to \(i\frac{d}{d\xi}\) and the operator \(\frac{d}{d x}\) of differentiation to multiplication by \(i\xi\). For the Fourier transform on the Lobachevsky plane, we establish a similar correspondence for a certain family of differential operators. It appears that differential operators on the Lobachevsky

Spaces of Dyadic Distributions Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210601
M. A. Karapetyants, V. Yu. ProtasovAbstract This paper studies spaces of distributions on a dyadic halfline, which is the positive halfline equipped with bitwise binary addition and Lebesgue measure. We prove the nonexistence of a space of dyadic distributions which satisfies a number of natural requirements (for instance, the property of being invariant with respect to the Walsh–Fourier transform) and, in addition, is invariant with

Differential Inclusions with Mixed Semicontinuity Properties in a Banach Space Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210307
A. A. TolstonogovAbstract A differential inclusion whose righthand side is the sum of two setvalued mappings in a separable Banach space is considered. The values of the first mapping are bounded and closed but not necessarily convex, and this mapping is Lipschitz continuous in the phase variable. The values of the second one are closed, and this mapping has mixed semicontinuity properties: given any phase point

A Remark on the Interpolation Inequality between Sobolev Spaces and Morrey Spaces Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210307
MinhPhuong Tran, ThanhNhan NguyenAbstract Interpolation inequalities play an important role in the study of PDEs and their applications. There are still some interesting open questions and problems related to integral estimates and regularity of solutions to elliptic and/or parabolic equations. The main purpose of our work is to provide an important observation concerning the \(L^p\)boundedness property in the context of interpolation

The Structure of the Algebra of Weak Jacobi Forms for the Root System $$F_4$$ Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210307
D. V. AdlerAbstract We prove the polynomiality of the bigraded ring \(J_{*,*}^{w, W}(F_4)\) of weak Jacobi forms for the root system \(F_4\) which are invariant with respect to the corresponding Weyl group. This work is a continuation of a joint article with V. A. Gritsenko, where the structure of the algebras of weak Jacobi forms related to the root systems of \(D_n\) type for \(2\leqslant n \leqslant 8\) was

Characters of the Infinite Symmetric Inverse Semigroup Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210307
N. I. NessonovAbstract A complete description of indecomposable characters of the infinite symmetric inverse semigroup is given. The method essentially uses the decomposition of the elements of this semigroup into a product of independent quasicycles and the multiplicativity theorem. Realizations of all factor representations of finite type are constructed.

Values of the $$\mathfrak{sl}_2$$ Weight System on Complete Bipartite Graphs Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210307
P. A. FilippovaAbstract A weight system is a function on chord diagrams that satisfies the socalled fourterm relations. Vassiliev’s theory of finiteorder knot invariants describes these invariants in terms of weight systems. In particular, there is a weight system corresponding to the colored Jones polynomial. This weight system can be easily defined in terms of the Lie algebra \(\mathfrak{sl}_2\), but this definition

On AlgebraicGeometric Methods for Constructing Submanifolds with Flat Normal Bundle and Holonomic Net of Curvature Lines Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210307
E. V. Glukhov, O. I. MokhovAbstract In this paper we propose a generalization of Krichever’s algebraicgeometric construction of orthogonal coordinate systems in a flat space. In the theory of integrable systems of hydrodynamic type a fundamental role is also played by orthogonal coordinates in some special nonflat spaces. The most important class of such spaces is given by metrics of submanifolds in flat spaces that have flat

Homogenization of the FourthOrder Elliptic Operator with Periodic Coefficients with Correctors Taken into Account Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20210307
V. A. Sloushch, T. A. SuslinaAbstract An elliptic fourthorder differential operator \(A_\varepsilon\) on \(L_2(\mathbb{R}^d;\mathbb{C}^n)\) is studied. Here \(\varepsilon >0\) is a small parameter. It is assumed that the operator is given in the factorized form \(A_\varepsilon = b(\mathbf{D})^* g(\mathbf{x}/\varepsilon) b(\mathbf{D})\), where \(g(\mathbf{x})\) is a Hermitian matrixvalued function periodic with respect to some

Interpolation of Protoquantum Spaces Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20200914
O. Yu. Aristov, N. V. VolosovaWe consider the complex interpolation method in the context of protoquantum spaces. We apply it to construct an ℒpprotoquantization of an arbitrary normed space for 1 < p < ∞.

The Essential Spectrum of OneDimensional Dirac Operators with Delta Interactions Funct. Anal. Its Appl. (IF 0.507) Pub Date : 20200914
V. S. RabinovichWe describe the location of the essential spectrum of onedimensional Dirac operators with singular potentials supported on discrete sets in ℝ in terms of limit operators.