Recent Papers

On interpolation and zeros of power series whose sequence of coefficients belongs to $l^p$

This note studies interpolation by analytic functions in the unit disk whose Taylor coefficients belong to l^p, with emphasis on the image of l_A^1 on subsets of the disk and on zero sets for l_A^p when p is greater than 2. It proves that any Carleson set contained in the open disk is finite, and fo…

On the Representation of Arbitrary Functions by Dirichlet Series

The paper studies when arbitrary functions analytic in a convex domain can be represented by Dirichlet series with complex exponents, noting first that such representation is impossible when the exponents lie on only one or two rays. It proves a representation theorem using an entire function of exp…

On the spectral decomposition of arbitrary self-adjoint operators in terms of eigenfunctionals

This note develops a general construction of spectral expansions in eigenfunctionals for self-adjoint operators in Hilbert space, including operators with continuous spectrum and without prior restrictions on the spectral family or the structure of the space. Using boundary limits of expressions for…

ON THE THEORY OF GENERALIZED SOLVABLE GROUPS\*

This note studies generalized solvability conditions in group theory through the introduction of weakly normal subgroups and related uniform and weakly normal series. It establishes analogues of the normalizer condition for periodic groups, finite groups, and groups possessing ascending series with …

On a Family of Differential Survival Games in the Space $R^n$

This paper studies a family of antagonistic differential games modeling pursuit and survival in a closed convex subset of Euclidean space, where a faster pursuer and a slower evader may continuously choose directions of motion. It formalizes admissible pure strategies, defines capture and escape pay…

On the Behavior at Infinity of Eigenfunctions of the Schrödinger Operator

The paper studies the behavior at infinity of spectral kernels and eigenfunctions for arbitrary self-adjoint extensions of the Schrödinger operator in Euclidean space with a smooth potential, without assuming semiboundedness. It proves growth estimates for the spectral kernel, valid for almost every…

ON SOME LIMITING PROPERTIES OF ORTHOGONAL POLYNOMIALS

On the Approximation of Stepanov Almost Periodic Functions

This note studies approximation of Stepanov almost periodic functions by uniformly almost periodic functions and entire functions of bounded degree, using convolution kernels with controlled Fourier transforms. It establishes estimates in the Stepanov metric for truncated spectral approximants, rela…

An upper bound for the entropy of a classical dynamical system

This paper proves an upper bound for the entropy of a classical dynamical system, defined as a measure-preserving diffeomorphism of a compact Riemannian manifold. The argument relates entropy growth for finite smooth partitions to the growth of boundary area, using an entropy inequality for probabil…

ON THE ELEMENTARY THEORY OF MAXIMAL NORMED FIELDS

The paper studies elementary theories of maximal non-Archimedean normed fields, formulated as structures consisting of a field, valuation, and value group. After introducing algebraic completeness and pseudo-convergent completeness, it establishes isomorphism and elementary equivalence criteria show…

On the Theory of Topological Groups

This paper studies locally bicompact topological groups, focusing on the relation between local projective nilpotence, bicompact generation, and the structure of bicompact elements. It proves that every bicompactly generated locally projectively nilpotent group is projectively nilpotent, hence proje…

An application of a theorem of H. Cartan to mathematical statistics

This paper applies Cartan’s theorem A, through the finite generation of ideals of holomorphic functions on a compact simply connected polycylinder, to questions in mathematical statistics. It considers families of statistics connected by parameters whose generalized moments depend holomorphically on…

Asymptotic Formulas for the Eigenvalues of an Elliptic Membrane

The paper studies the asymptotic distribution of eigenvalues for the Laplacian on an elliptical membrane under Dirichlet and Neumann boundary conditions. By separating variables in elliptic coordinates, the problem is reduced to asymptotic analysis of Mathieu equations, followed by counting lattice …

AUTOMATON SUBSTITUTIONS AND WREATH PRODUCTS OF GROUPS

The paper studies groups of one-to-one automaton mappings of words over an n-letter alphabet and their finite-automaton subgroups through the structure of automaton substitutions on words of fixed length. It introduces a dual form of the wreath product, proves that each group of substitutions on wor…

ON PERIODIC REGIMES OF SOME DISTRIBUTED SYSTEMS

This paper studies periodic regimes in distributed diffusion systems motivated by self-oscillations in electrochemical processes with nonlinear boundary behavior at an electrode. It derives explicit periodic solutions of the diffusion equation on a semi-infinite domain for piecewise linear boundary …

CONDITIONS FOR DISCRETENESS AND CONTINUITY OF THE SPECTRUM IN THE CASE OF A SELF-ADJOINT SYSTEM OF DIFFERENTIAL EQUATIONS OF EVEN ORDER

Topological Equivalence of Certain Cones in a Banach Space

This paper studies the topological structure of cones in Banach spaces, especially cones generated by bases or minimal systems. It proves that in a separable Banach space every normal cone can be made strongly acute by an equivalent norm, using an embedding into a space of continuous functions and a…

Application of Path Integrals to the Derivation of Short-Wavelength Asymptotics in Diffraction Problems

The paper proposes the use of continual integral representations to obtain short-wave asymptotics for stationary diffraction problems in exterior domains with smooth convex obstacles. The Green function of the stationary problem is related to the heat Green function, which is represented on a two-sh…

INTEGRAL CURVES OF A CERTAIN DIFFERENTIAL EQUATION

ON THE QUESTION OF COMPLETE CONTINUITY OF INTEGRAL OPERATORS

This note studies complete continuity of integral operators acting between ordered function spaces of classes related to \(KB\)-spaces and their duals. It introduces strong complete continuity, defined through compactness with a common order regulator, and relates this notion to \((b,o)\)-linear ope…

The Cauchy Problem for a Linear Differential Equation of Infinite Order

This paper studies Cauchy problems for linear differential equations of infinite order with constant coefficients, including homogeneous and nonhomogeneous equations whose characteristic function is an entire function with simple zeros satisfying specified product and growth conditions. It formulate…

Some Criteria for Stability of Functionals

The paper studies linear functionals on algebraic polynomials specified by their moments and develops criteria for estimating the number of their true nodes, a quantity related to stability in a parameter interval. Using conditional nodes, resolvents, and weights, it proves a sufficient condition en…

On an Optimal Cubature Lattice for Isotropically Smooth Functions of Two Variables

This note studies optimal two-dimensional lattices for cubature formulas for smooth functions, where optimality is defined by minimizing the absolutely convergent sum of inverse even powers of distances over lattices of fixed fundamental volume. Building on Sobolev’s connection between such lattices…

On the Fourier Transform in Besov Spaces. The Zero Scale $B^0_{p,\theta}$

The paper studies Besov spaces with possibly nonpositive smoothness from the viewpoint of the Fourier transform, with special emphasis on the zero scale \(B^0_{p,\theta}\). Using lacunary decompositions of the Fourier domain, it gives equivalent norms for anisotropic Besov spaces, extends the defini…

Linear Transformations of Directionally Divergent Sequences

This note studies linear transformations of unbounded complex sequences that diverge to infinity within prescribed half-strips or angles in the complex plane. For regular matrices with finite rows, it gives necessary and sufficient conditions under which such transformations preserve the original re…

On a Certain Class of Integro-Differential Equations

APPLICATION OF THE THEOREM ON DIFFERENTIAL INEQUALITIES TO THE GOURSAT PROBLEM FOR A LINEAR SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS

On the Uniqueness of the Solution of a Two-Layer One-Phase Stefan-Type Problem

The paper proves uniqueness for a two-layer one-phase Stefan-type free boundary problem modeling crystallization of a melt in contact with an immersed refractory plate, with discontinuous thermal coefficients and transmission conditions at the material interface. The argument assumes existence of an…

SEMIGROUPS OF RECTANGULAR BINARY RELATIONS

The paper studies semigroups formed by rectangular binary relations and relates them to matrix partial operatives and matrix 0-bands. It defines an associative construction from a dense binary relation, proves a representation theorem for matrix 0-bands as such constructions with an adjoined zero, a…

A GENERALIZATION OF E. SKLYARENKO’S THEOREM

This paper generalizes Sklyarenko’s theorem on embedding a normal space into a bicompact extension of the same weight and dimension. It introduces combinatorial properties defined by the possibility of refining finite open covers to covers whose nerves belong to prescribed families of finite complex…

On the Properties of Sums of Certain Sine and Cosine Series

This paper studies positivity, zeros, and lower estimates for sums of trigonometric series whose coefficients satisfy monotonicity and finite difference conditions. It generalizes earlier results of Fejér and others by replacing pointwise nonnegativity of higher differences with nonnegativity of cer…

On the Question of Oscillation of Solutions of Nonlinear Differential Equations

ON THE STABILITY OF DISCONTINUOUS SYSTEMS WITH ALMOST REDUCIBLE LINEAR APPROXIMATIONS

ON THE EIGENFUNCTIONS OF THE EQUATION \(\Delta u+\lambda f(u)=0\)

The paper studies existence and nonexistence of eigenfunctions for the nonlinear Dirichlet problem Δu + λf(u) = 0 in bounded domains. For dimensions n > 2, it proves existence under a subcritical growth condition on f using a constrained variational minimization argument and Sobolev compactness, and…

On the topological structure of stability regions of a self-adjoint system of differential equations with periodic coefficients

This paper studies the topological structure of strong stability regions for real self-adjoint first-order systems of differential equations with periodic coefficients, generalizing Hamiltonian systems. Using a characterization of admissible matriciants by symplectic endpoint conditions, the authors…

General Boundary Value Problems for Parabolic Equations in a Closed Domain

This paper studies general boundary value problems for parabolic differential equations in bounded domains whose smooth boundary has distinguished points where the tangent plane is perpendicular to the time axis. It formulates weighted anisotropic Sobolev spaces adapted to the parabolic scaling, red…

Stability of Difference Schemes for the Cauchy Problem for Systems of Partial Differential Equations

The paper studies stability of finite difference schemes for the Cauchy problem for linear systems of partial differential equations with constant coefficients that are correct in the sense of Petrovskii. Using Fourier analysis in Sobolev norms for periodic initial data, it proves stability of an ex…

ON A PROPERTY OF “INSTABILITY” OF HARMONIC CAPACITY

This note studies an instability property of Newtonian harmonic capacity for open subsets of three-dimensional Euclidean space and its consequences for uniform approximation by harmonic functions. It shows that if the local capacity of an open set is sufficiently large in a limsup sense at almost ev…

The Cauchy Problem and a Boundary Value Problem for Some Nonlinear Second-Order Ordinary Differential Equations

This note studies Cauchy and boundary-value problems for several singular nonlinear second-order ordinary differential equations on the half-line, including equations related by a radial substitution and arising in spherically symmetric scalar-field models. It analyzes when solutions can change sign…

ON BOUNDARY-VALUE PROBLEMS FOR DIFFERENTIAL AND INTEGRO-DIFFERENTIAL EQUATIONS IN THE SPACES \(W_{p_1\ldots p_k}^{m_1\ldots m_k}\), \(W_{p_1\ldots p_k,b_1\ldots b_n}^{m_1\ldots m_k}\)

The paper studies boundary value problems for differential and integro-differential equations associated with mixed Sobolev-type spaces and their weighted analogues, including cases that lead to degenerate equations. It establishes trace and compact embedding properties for these spaces on boundary …

Locally bicompact rings without zero divisors

This paper studies locally bicompact rings with identity and without zero divisors, focusing on the totally disconnected case beyond the known classification of locally bicompact division rings. It proves that locally bicompact normed rings of this type are either division rings or bicompact local r…

ON THE DIFFERENCE BETWEEN THE METHOD OF EXPANSION IN A SERIES WITH RESPECT TO A PARAMETER AND THE METHOD OF SUCCESSIVE APPROXIMATIONS IN SOLVING NONLINEAR INTEGRAL EQUATIONS

On the dimension of remainders in compact extensions

This paper studies dimension-theoretic properties of remainders in compact extensions of metrizable spaces with countable bases. It proves that if X is compact and Y is not locally compact, then every compact extension of X × Y has a remainder of dimension at least dim X, yielding consequences for p…

Periods of $\mathfrak{A}$-closed forms

This paper introduces periods for forms closed with respect to a generalized differential operator on a compact real analytic Riemannian manifold. Using bilinear differential forms associated with solutions of adjoint equations, it defines period pairings with cycles and proves an isomorphism betwee…

CONDITIONS FOR DISCRETENESS AND CONTINUITY OF THE SPECTRUM IN THE CASE OF A SELF-ADJOINT SYSTEM OF FIRST-ORDER DIFFERENTIAL EQUATIONS

This paper studies the spectral type of self-adjoint first-order differential systems on the real line with constant real diagonal principal matrix and continuous Hermitian potential. It derives sufficient criteria for discreteness of the spectrum using quadratic estimates and a splitting principle,…

ON THE SOLUTION OF REGULARIZED EQUATIONS IN PERTURBATION THEORY

On Conditions for a Center

On the Stability of Solutions of the Cauchy Problem for Linear Differential Equations of Hyperbolic Type

This paper studies stability of solutions to the Cauchy problem for linear hyperbolic differential equations with values in a complex Banach space and constant bounded operator coefficients. The argument reformulates the boundary-value problem as an operator equation using integral operators, repres…

On an integral equation on the half-line in a class of functions growing at infinity

The paper studies a linear integral equation on the half-axis with kernels depending on the difference and sum of variables, in weighted classes of functions allowed to grow at infinity. Using weighted convolution rings, generalized Fourier transforms, Fredholm operator theory, and reductions to Rie…

ON THE CONTINUAL PRODUCT OF LEBESGUE SPACES

This note studies when a probability measure space is isomorphic to the product of continuum many unit intervals with Lebesgue measure. It formulates conditions involving completeness with respect to null subsets, homogeneity, equality of metric and exact weights with the continuum cardinal, and a c…