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Two-Dimensional Diffusion Orthogonal Polynomials Ordered by a Weighted Degree Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2024-03-12 S. Yu. Orevkov
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Resurgence and Partial Theta Series Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2024-03-12 Li Han, Yong Li, David Sauzin, Shanzhong Sun
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Linear and Multiplicative Maps under Spectral Conditions Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2024-03-12 Bhumi Amin, Ramesh Golla
Abstract The multiplicative version of the Gleason–Kahane–Żelazko theorem for \(C^*\)-algebras given by Brits et al. in [4] is extended to maps from \(C^*\)-algebras to commutative semisimple Banach algebras. In particular, it is proved that if a multiplicative map \(\phi\) from a \(C^*\)-algebra \(\mathcal{U}\) to a commutative semisimple Banach algebra \(\mathcal{V}\) is continuous on the set of
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Resolution of Singularities of the Odd Nilpotent Cone of Orthosymplectic Lie Superalgebras Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2024-03-12 I. D. Motorin
Abstract We construct a Springer-type resolution of singularities of the odd nilpotent cone of the orthosymplectic Lie superalgebras \(\mathfrak{osp}(m|2n)\).
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Limit Spectral Measures of Matrix Distributions of Metric Triples Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-12-29 A. M. Vershik, F. V. Petrov
Abstract The notion of the limit spectral measure of a metric triple (i.e., a metric measure space) is defined. If the metric is square integrable, then the limit spectral measure is deterministic and coincides with the spectrum of the integral operator on \(L^2(\mu)\) with kernel \(\rho\). An example in which there is no deterministic spectral measure is constructed.
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The Quasilinear Parabolic Venttsel’ Problem with Discontinuous Leading Coefficients Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-12-29 D. E. Apushkinskaya, A. I. Nazarov, D. K. Palagachev, L. G. Softova
Abstract New results on the strong solvability in Sobolev spaces of the quasilinear Venttsel’ problem for parabolic equations with discontinuous leading coefficients are obtained.
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Some Inequalities for $$p$$ -Quermassintegrals Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-12-29 Weidong Wang, Yanping Zhou
Abstract In this paper, we generalize the notions of quermassintegrals, harmonic quermassintegrals, and affine quermassintegrals to \(p\)-quermassintegrals so that the cases \(p=1, -1, -n\) of \(p\)-quermassintegrals are quermassintegrals, harmonic quermassintegrals, and affine quermassintegrals, respectively. Further, we obtain some inequalities associated with \(p\)-quermassintegrals, including \(L_q\)
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On the Birman Problem in the Theory of Nonnegative Symmetric Operators with Compact Inverse Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-12-29 M. M. Malamud
Abstract Large classes of nonnegative Schrödinger operators on \(\Bbb R^2\) and \(\Bbb R^3\) with the following properties are described: 1. The restriction of each of these operators to an appropriate unbounded set of measure zero in \(\Bbb R^2\) (in \(\Bbb R^3\)) is a nonnegative symmetric operator (the operator of a Dirichlet problem) with compact preresolvent; 2. Under certain additional assumptions
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Spectral Analysis of a Dynamical System Describing the Diffusion of Neutrons Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-12-29 S. A. Stepin
Abstract The spectral properties of the generator of an evolution semigroup describing the dynamics of particle transport in a substance are studied. An effective estimate of the number of unstable modes is obtained, and geometric conditions for spectral stability and instability are found.
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Multipliers for the Calderón Construction Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-12-29 E. I. Berezhnoi
Abstract On the basis of a new approach to the Calderón construction \(X_0^{\theta} X_1^{1-\theta}\) for ideal spaces \(X_0\) and \(X_1\) and a parameter \(\theta \in [0,1]\), final results concerning a description of multipliers spaces are obtained. In particular, it is shown that if ideal spaces \(X_0\) and \(X_1\) have the Fatou property, then \(M(X_0^{\theta_0} X_1^{1-\theta_0}\,{\to}\,X_0^{\theta_1}
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Diagram Automorphism Fixed Lie Algebras and Diagram Automorphism Fixed Quiver Varieties Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-12-29 Zhijie Dong, Haitao Ma
Abstract We define certain subvarieties, called \(\theta\)-Hecke correspondences, in Cartesian products of diagram automorphism fixed quiver varieties. These give us generators of diagram automorphism fixed Lie algebras.
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Singularities Equivariantly Simple with Respect to Irreducible Representations Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-09-05 I. A. Proskurnin
Abstract There are many papers on the classification of singularities that are invariant or equivariant under the action of a finite group. However, since the problem is difficult, most of these papers consider only special cases, for example, the case of the action of a particular group of small order. In this paper, an attempt is made to prove general statements about equivariantly simple singularities;
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Connes Integration Formula: A Constructive Approach Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-09-05 D. V. Zanin, F. A. Sukochev
Abstract A version of Connes Integration Formula which provides concrete asymptotics of eigenvalues is given. This radically extends the class of quantum-integrable functions on compact Riemannian manifolds.
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Asymptotic Relations for the Distributional Stockwell and Wavelet Transforms Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-09-05 J. V. Buralieva
Abstract Abelian- and Tauberian-type results characterizing the quasiasymptotic behavior of distributions in \(\mathcal{S}_{0}'(\mathbb{R})\) in terms of their Stockwell transforms are obtained. An Abelian-type result relating the quasiasymptotic boundedness of Lizorkin distributions to the asymptotic behavior of their Stockwell transforms is given. Several asymptotic results for the distributional
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Improved Inequalities for Numerical Radius via Cartesian Decomposition Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-09-05 P. Bhunia, S. Jana, M. S. Moslehian, K. Paul
Abstract We derive various lower bounds for the numerical radius \(w(A)\) of a bounded linear operator \(A\) defined on a complex Hilbert space, which improve the existing inequality \(w^2(A)\geq \frac{1}{4}\|A^*A+AA^*\|\). In particular, for \(r\geq 1\), we show that $$\tfrac{1}{4}\|A^*A+AA^*\|\leq\tfrac{1}{2}(\tfrac{1}{2}\|\operatorname{Re}(A)+\operatorname{Im}(A)\|^{2r}+\tfrac{1}{2}\|\operatorn
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On a Sharp Lower Bound for the Tjurina Number of Zero-Dimensional Complete Intersections Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-09-05 A. G. Aleksandrov
Abstract As is known, for isolated hypersurface singularities and complete intersections of positive dimension, the Milnor number is the least upper bound for the Tjurina number, i.e., \(\tau \leqslant \mu\). In this paper we show that, for zero-dimensional complete intersections, the reverse inequality holds. The proof is based on properties of faithful modules over an Artinian local ring. We also
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A Remark on Davies’ Hardy Inequality Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-09-05 Y. C. Huang
Abstract We give an “integration by parts” approach to Davies’ Hardy inequality. An improvement with a strictly larger Hardy weight is thereby obtained.
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On the Structure of Coset $$n$$ -Valued Topological Groups on $$S^3$$ and $$\mathbb{R}P^3$$ Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-09-05 D. V. Gugnin
Abstract Three-dimensional manifolds carrying the structure of \(n\)-valued coset topological groups originating from the Lie groups \(Sp(1)\) and \(SO(3)\) are classified.
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The Image of a Lagrangian Germ of Type $$E_6^\pm$$ Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-09-05 V. D. Sedykh
Abstract It is proved that the image of a stable germ of type \(E_6^\pm\) of a Lagrangian map to \(\mathbb R^n\) is homeomorphic to the germ at zero of a closed half-space.
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The Weak Solvability of an Inhomogeneous Dynamic Problem for a Viscoelastic Continuum with Memory Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-09-05 V. G. Zvyagin, V. P. Orlov
Abstract The existence of a weak solution to the initial boundary value problem for the equations of motion of a viscoelastic fluid with memory along the trajectories of a nonsmooth velocity field with inhomogeneous boundary condition is proved. The analysis involves Galerkin-type approximations of the original problem followed by the passage to the limit based on a priori estimates. To study the behavior
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Self-Joinings and Generic Extensions of Ergodic Systems Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-09-01
Abstract It is proved that the generic extensions of a dynamical system inherit the triviality of pairwise independent self-joinings. This property is related to well-known problems of joining theory and to Rokhlin’s famous multiple mixing problem.
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A Convergence Rate Estimate for Remotest Projections on Three Subspaces Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-06-01
Abstract We give an estimate of the rate of convergence to zero of the norms of remotest projections on three subspaces of a Hilbert space with zero intersection for starting vectors in the sum of orthogonal complements to these subspaces.
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A Semigroup of Paths on a Sequence of Uniformly Elliptic Complexes Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-06-01
Abstract The work is devoted to solving a problem of L. N. Shevrin and M. V. Sapir (Question 3.81b of the Sverdlovsk Notebook), namely, to constructing a finitely presented infinite nil-semigroup satisfying the identity \(x^9 = 0\) . This problem is solved with the help of geometric methods of the theory of tilings and aperiodic tessellations. A semigroup of paths on a tiling, under certain conditions
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Hermitian Property and the Simplicity of Spectrum of Bethe Subalgebras in Yangians Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-04-13 I. A. Mashanova-Golikova
Abstract The image of the Bethe subalgebra \(B(C)\) in the tensor product of representations of the Yangian \(Y(\mathfrak{gl}_n)\) contains the full set of Hamiltonians of the Heisenberg magnet chain XXX. The main problem in the XXX integrable system is the diagonalization of the operators by which the elements of Bethe subalgebras act on the corresponding representations of the Yangian. The standard
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On an Elliptic Operator Degenerating on the Boundary Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-04-13 V. E. Nazaikinskii
Abstract Let \(\Omega\subset\mathbb{R}^n\) be a bounded domain with smooth boundary \(\partial\Omega\), let \(D(x)\in C^\infty(\overline\Omega)\) be a defining function of the boundary, and let \(B(x)\in C^\infty(\overline\Omega)\) be an \(n\times n\) matrix function with self-adjoint positive definite values \(B(x )=B^*(x)>0\) for all \(x\in\overline\Omega\) The Friedrichs extension of the minimal
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Unitary Flows with Tensor Simple Spectrum Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-04-13 V. V. Ryzhikov
Abstract Unitary flows \(T_t\) of dynamical origin such that, for any countable \(Q\subset (0,+\infty)\), the spectrum of the tensor product \(\bigotimes_{q\in Q} T_q \) is simple are constructed. All typical flows preserving a sigma-finite measure have this property.
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Approximations of the Images and Integral Funnels of the $$L_p$$ Balls under a Urysohn-Type Integral Operator Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-04-13 A. Huseyin, N. Huseyin, Kh. G. Guseinov
Abstract Approximations of the image and integral funnel of a closed ball of the space \(L_p\), \(p>1\), under a Urysohn-type integral operator are considered. A closed ball of the space \(L_p\), \(p>1\), is replaced by a set consisting of a finite number of piecewise constant functions, and it is proved that, for appropriate discretization parameters, the images of these piecewise constant functions
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On Bloch Solutions of Difference Schrödinger Equations Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-04-13 D. I. Borisov, A. A. Fedotov
Abstract Bloch solutions of the difference Schrödinger equation with periodic complex potential on the real line are discussed. The case where the spectral parameter is outside the spectrum of the corresponding Schrödinger operator is considered.
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Superposition Principle for the Fokker–Planck–Kolmogorov Equations with Unbounded Coefficients Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-04-13 T. I. Krasovitskii, S. V. Shaposhnikov
Abstract The superposition principle delivers a probabilistic representation of a solution \(\{\mu_t\}_{t\in[0, T]}\) of the Fokker–Planck–Kolmogorov equation \(\partial_t\mu_t=L^{*}\mu_t\) in terms of a solution \(P\) of the martingale problem with operator \(L\). We generalize the superposition principle to the case of equations on a domain, examine the transformation of the measure \(P\) and the
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One-Dimensional Central Measures on Numberings of Ordered Sets Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-04-13 A. M. Vershik
Abstract We describe one-dimensional central measures on numberings (tableaux) of ideals of partially ordered sets (posets). As the main example, we study the poset \(\mathbb{Z}_+^d\) and the graph of its finite ideals, multidimensional Young tableaux; for \(d=2\), this is the ordinary Young graph. The central measures are stratified by dimension; in the paper we give a complete description of the
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Restricted Partitions: The Polynomial Case Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-04-13 V. L. Chernyshev, T. W. Hilberdink, D. S. Minenkov, V. E. Nazaikinskii
Abstract We prove a restricted inverse prime number theorem for an arithmetical semigroup with polynomial growth of the abstract prime counting function. The adjective “restricted” refers to the fact that we consider the counting function of abstract integers of degree \(\le t\) whose prime factorization may only contain the first \(k\) abstract primes (arranged in nondescending order of their degree)
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On Maximal Extensions of Nilpotent Lie Algebras Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-04-13 V. V. Gorbatsevich
Abstract Extensions of finite-dimensional nilpotent Lie algebras, in particular, solvable extensions, are considered. Some properties of maximal extensions are proved. A counterexample to L. Šnobl’s conjecture concerning the uniqueness of maximal solvable extensions is constructed.
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Improved Resolvent Approximations in Homogenization of Second-Order Operators with Periodic Coefficients Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-04-13 S. E. Pastukhova
Abstract For elliptic divergent self-adjoint second-order operators with \(\varepsilon\)-periodic measurable coefficients acting on the whole space \(\mathbb{R}^d\), resolvent approximations in the operator norm \(\|\!\,\boldsymbol\cdot\,\!\|_{H^1\to H^1}\) with remainder of order \(\varepsilon^2\) as \(\varepsilon\to 0\) are found by the method of two-scale expansions with the use of smoothing.
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On the Extension of Functions from Countable Subspaces Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-04-13 A. Yu. Groznova
Abstract Three intermediate class of spaces \(\mathscr{R}_1\subset \mathscr{R}_2\subset \mathscr{R}_3\) between the classes of \(F\)- and \(\beta\omega\)-spaces are considered. The \(\mathscr{R}_1\)- and \(\mathscr{R}_3\)-spaces are characterized in terms of the extension of functions. It is proved that the classes of \(\mathscr{R}_1\)-, \(\mathscr{R}_2\)-, \(\mathscr{R}_3\)-, and \(\beta\omega\)-spaces
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Semifinite Harmonic Functions on the Zigzag Graph Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-01-31 N. A. Safonkin
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Criteria for the Property (UWE) and the a-Weyl Theorem Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-01-31 Chenhui Sun, Xiaohong Cao
Abstract In this paper, the property (UWE) and the a-Weyl theorem for bounded linear operators are studied in terms of the property of topological uniform descent. Sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space to have the property (UWE) and satisfy the a-Weyl theorem are established. In addition, new criteria for the fulfillment of the property (UWE) and
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Cyclic Vectors and Invariant Subspaces of the Backward Shift Operator in Schwartz Modules Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-01-31 O. A. Ivanova, S. N. Melikhov
Abstract Cyclic vectors and proper closed invariant subspaces of the backward shift operator in the Schwartz modules of entire functions of exponential type are described. The results are applied to describe ideals of the algebra of infinitely differentiable functions on a closed or open interval containing \(0\) with Duhamel product as multiplication.
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Parametric Korteweg–de Vries Hierarchy and Hyperelliptic Sigma Functions Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-01-31 E. Yu. Bunkova, V. M. Bukhshtaber
Abstract In this paper, a parametric Korteweg–de Vries hierarchy is defined that depends on an infinite set of graded parameters \(a = (a_4,a_6,\dots)\). It is shown that, for any genus \(g\), the Klein hyperelliptic function \(\wp_{1,1}(t,\lambda)\) defined on the basis of the multidimensional sigma function \(\sigma(t, \lambda)\), where \(t = (t_1, t_3,\dots, t_{2g-1})\) and \(\lambda = (\lambda_4
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Taylor Spectrum for Modules over Lie Algebras Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-01-31 B. I. Bilich
Abstract In this paper we generalize the notion of the Taylor spectrum to modules over an arbitrary Lie algebra and study it for finite-dimensional modules. We show that the spectrum can be described as the set of simple submodules in the case of nilpotent and semisimple Lie algebras. We also show that this result does not hold for solvable Lie algebras and obtain a precise description of the spectrum
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On Poisson Semigroup Hypercontractivity for Higher-Dimensional Spheres Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2023-01-31 Yi. C. Huang
Abstract In this note we consider a variant of a question of Mueller and Weissler raised in 1982, thereby complementing a classical result of Beckner on Stein’s conjecture and a recent result of Frank and Ivanisvili. More precisely, we show that, for \(1
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Estimation of the Modulus of Hölder Metric Regularity Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-10-10 Wending Xu
Abstract This paper mainly studies the modulus of Hölder metric regularity. The concepts of a generalized \(p\)-order Clarke-like set and generalized graphical derivative are introduced and used to estimate this modulus. The main result implies that it is bounded above by the upper limit of the inner norm of the inverse of generalized graphical derivative.
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Distributions of Polynomials in Gaussian Random Variables under Constraints on the Powers of Variables Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-10-10 E. D. Kosov
Abstract We study the densities of measures that are polynomial images of the standard Gaussian measure on \(\mathbb{R}^n\). We assume that the degree of a polynomial is fixed and each variable appears in the monomials of the polynomial to powers bounded by another fixed number.
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On the Arens Homomorphism Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-10-10 B. Turan, M. Aslantaş
Abstract Let \(E\) be a unital \(f\)-module over an \(f\)-algebra \(A\). With the help of Arens extension theory, a \((A^{\sim})_{n}^{\sim}\) module structure on \(E^{\sim}\) can be defined. The paper deals mainly with properties of the Arens homomorphism \(\eta\colon(A^{\sim})_{n}^{\sim}\to \operatorname {Orth}(E^{\sim})\), which is defined by the \((A^{\sim})_{n}^{\sim}\) module structure on \(E^{\sim}\)
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$$A$$ -Ergodicity of Convolution Operators in Group Algebras Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-10-10 H. Mustafaev, A. Huseynli
Abstract Let \(G\) be a locally compact Abelian group with dual group \(\Gamma \), let \(\mu\) be a power bounded measure on \(G\), and let \(A=[ a_{n,k}]_{n,k=0}^{\infty}\) be a strongly regular matrix. We show that the sequence \(\{\sum_{k=0}^{\infty}a_{n,k}\mu^{k}\ast f\}_{n=0}^{\infty}\) converges in the \(L^{1}\)-norm for every \(f\in L^{1}(G)\) if and only if \(\mathcal{F}_{\mu}:=\{\gamma \in
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Extension Operator for Subspaces of Vector Spaces over the Field $$\mathbb{F}_2$$ Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-10-10 O. V. Sipacheva, A. A. Solonkov
Abstract In is proved that the free topological vector space \(B(X)\) over the field \(\mathbb{F}_2=\{0,1\}\) generated by a stratifiable space \(X\) is stratifiable, and therefore, for any closed subspace \(F\subset B(X)\) (in particular, for \(F=X\)) and any locally convex space \(E\), there exists a linear extension operator \(C(F,E)\to C(B(X),E)\) between spaces of continuous maps.
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Newton Polytopes of Nondegenerate Quadratic Forms Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-10-10 A. Yu. Yuran
Abstract We characterize Newton polytopes of nondegenerate quadratic forms and Newton polyhedra of Morse singularities.
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Pointwise Conditions for Membership of Functions in Weighted Sobolev Classes Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-10-10 V. I. Bogachev
Abstract According to a known characterization, a function \(f\) belongs to the Sobolev space \(W^{p,1}(\mathbb{R}^n)\) of functions contained in \(L^p(\mathbb{R}^n)\) along with their generalized first-order derivatives precisely when there is a function \(g\in L^p(\mathbb{R}^n)\) such that $$|f(x)-f(y)|\le |x-y|(g(x)+g(y))$$ for almost all pairs \((x,y)\). An analogue of this estimate is also known
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Approximation of Operator Semigroups Using Linear-Fractional Operator Functions and Weighted Averages Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-10-10 J. L. Rogava
Abstract An analytic semigroup of operators on a Banach space is approximated by a sequence of positive integer powers of a linear-fractional operator function. It is proved that the order of the approximation error in the domain of the generating operator equals \(O(n^{-2}\ln(n))\). For a self-adjoint positive definite operator \(A\) decomposed into a sum of self-adjoint positive definite operators
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Extended Spectra for Some Composition Operators on Weighted Hardy Spaces Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-10-10 I. F. Z. Bensaid, F. León-Saavedra, P. Romero de la Rosa
Abstract Let \(\alpha\) be a complex scalar, and let \(A\) be a bounded linear operator on a Hilbert space \(H\). We say that \(\alpha\) is an extended eigenvalue of \(A\) if there exists a nonzero bounded linear operator \(X\) such that \(AX=\alpha XA\). In weighted Hardy spaces invariant under automorphisms, we completely compute the extended eigenvalues of composition operators induced by linear
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Wold-Type Decompositions for Pairs of Commutative Semigroups Generated by Isometries Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-07-29 T. Bînzar, C. Lăzureanu
Abstract In this paper we analyze connections between Wold-type decompositions of bi/isometries and pairs of semigroups of isometries, where at least one of semigroups is a product semigroup generated by two isometries.
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On the Milnor and Tjurina Numbers of Zero-Dimensional Singularities Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-07-29 A. G. Aleksandrov
Abstract In this paper we study relationships between some topological and analytic invariants of zero-dimensional germs, or multiple points. Among other things, it is shown that there exist no rigid zero-dimensional 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
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Strengthening of the Bourgain–Kontorovich Theorem on Small Values of Hausdorff Dimension Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-07-29 I. D. Kan
Abstract 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
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Two-Sided Estimates of the $$K$$ -Functional for Spaces of Functions of Generalized Bounded Variation Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-07-29 E. I. Berezhnoi
Abstract A two-sided 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
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Polynomials in the Differentiation Operator and Formulas for the Sums of Certain Convergent Series Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-07-29 K. A. Mirzoev, T. A. Safonova
Abstract 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 self-adjoint problem generated by the differential expression \(l_n[y]=P_n(i\,d/dx) y\) and the
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A Hilbert $$C^*$$ -Module with Extremal Properties Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-07-29 D. V. Fufaev
Abstract 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.
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On a Notion of Averaged Mappings in $$\operatorname{CAT}(0)$$ Spaces Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-07-29 A. Bërdëllima
Abstract 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 \(x_n:=Tx_{n-1}\) of a nonexpansive mapping \(T\) converge weakly to an element in \(\operatorname{Fix}
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Resonances for the Dirac Operator on the Half-Line Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-03-17 E. L. Korotyaev, D. S. Mokeev
Abstract We consider the inverse problem for a massless Dirac operator on the half-line 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.
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Note on Derivations of Certain non-CSL Algebras Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-03-17 Chaoqun Chen, Fangyan Lu
Abstract 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.
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Dunkl Translations, Dunkl-Type BMO Space, and Riesz Transforms for the Dunkl Transform on $$L^\infty$$ Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-03-17 Wentao Teng
Abstract In this paper we will give some results on the support of Dunkl translations on compactly supported functions. Then we will define the Dunkl-type 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 Dunkl-type BMO space under the assumption of the uniform boundedness of Dunkl translations. The proof
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Infinitesimal Center Problem on Zero Cycles and the Composition Conjecture Funct. Anal. Its Appl. (IF 0.4) Pub Date : 2022-03-17 A. Álvarez, J. L. Bravo, C. Christopher, P. Mardešić
Abstract 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