Showing 50 of 5847 papers in Mathematics

Description of Extensions of Hermitian Positive Functions

Unknown
1964 SovietRxiv: ru-196401.33283

The paper addresses the problem of describing all Hermitian positive extensions to the whole plane of a continuous Hermitian positive function initially given in a horizontal strip. It constructs spectral measures and associated canonical, or channel, positive-definite functions, proving an integral…

On Complete Systems of Convergence

Unknown
1964 SovietRxiv: ru-196401.33118

The paper addresses whether a complete orthonormal system of uniformly bounded functions can be a system of convergence, meaning that every square summable coefficient sequence yields an almost everywhere convergent orthogonal series. It constructs such a system on the unit interval by modifying Haa…

Elliptic Problems with Nonhomogeneous Boundary Conditions and Local Improvement of Regularity up to the Boundary for Generalized Solutions

Unknown
1964 SovietRxiv: ru-196401.32210

The paper studies elliptic boundary value problems with nonhomogeneous boundary conditions for properly elliptic operators on bounded domains. It introduces Sobolev-type spaces with boundary trace norms adapted to low and negative smoothness, and proves a homeomorphism theorem for the operator mappi…

On a Boundary Value Problem for Equations of Mixed Type

B. V. Melent'ev
1964 SovietRxiv: ru-196401.31940

This paper studies a Hilbert-Poincare boundary-value problem for the Tricomi equation in a domain composed of an elliptic part above the degeneracy line and a hyperbolic part bounded by characteristics below it. The argument reduces the mixed-type problem, using the Tricomi problem and gluing condit…

Partial topological products

Unknown
1964 SovietRxiv: ru-196401.31922

The paper introduces partial topological products, a construction that generalizes Tychonoff products by attaching fibers only over specified open subsets of a base space. It defines the construction, establishes basic preservation and dimension properties, including conditions for compactness, regu…

On Factor Mappings of Metric Spaces

Unknown
1964 SovietRxiv: ru-196401.31105

This paper studies when quotient images of metrizable spaces remain metrizable under special classes of mappings, including regular, uniform, bicompact, pseudo-open, monotone, and closed mappings. It introduces \(k_n\)-spaces and gives criteria showing, for example, that a regular quotient image of …

On Some Differential Games

Unknown
1964 SovietRxiv: ru-196401.30989

This paper studies a class of differential games in which the state evolves by analytic ordinary differential equations with two controls, and the objective is to reach a prescribed manifold in minimal time under an opposing control. Using Pontryagin-style adjoint variables and extremal trajectories…

On conditions for solvability of the abstract Cauchy problem

Unknown
1964 SovietRxiv: ru-196401.30726

The paper studies solvability of the abstract Cauchy problem \(dx(t)/dt=Ax(t)\), \(x(0)=x_0\), for a linear operator in a Banach space. It introduces a local Laplace transform suitable for finite time intervals and for infinite intervals without growth restrictions, proves uniqueness and inversion r…

On the Spectrum of Normal Operators and Their Perturbations

Unknown
1964 SovietRxiv: ru-196401.30690

This paper studies spectral localization for normal operators in Hilbert space and extends earlier perturbation results and lemmas of Glazman. It establishes dimension and codimension criteria relating bounds on the difference of two normal operators to the number of spectral points of one operator …

On a uniqueness theorem

Unknown
1964 SovietRxiv: ru-196401.30077

The paper proves uniqueness theorems for analytic and meromorphic functions in the unit disk belonging to refined Nevanlinna type classes defined by area growth conditions. Building on results of Carleson and integral representations of Dzhrbashyan, it shows that for functions in the classes \(T_\al…

On the Fisher–Welch–Wald Test

Unknown
1964 SovietRxiv: ru-196401.29474

This note studies the existence of similar Fisher, Welch, Wald tests for comparing the means of two normal populations with unknown and unequal variances, allowing samples of arbitrary sizes. Using Wald’s representation of the critical region and the analytic continuation of the similarity equation …

On the principle of limiting amplitude

Unknown
1964 SovietRxiv: ru-196401.29206

The paper studies the limiting amplitude principle for abstract second order evolution equations in a Hilbert space and for elliptic operators in unbounded domains. It first gives sufficient spectral resolvent conditions under which the time harmonic response with zero initial data converges, or has…

On the Magnitudes of Defects of a Meromorphic Function

V. P. Petrenko
1964 SovietRxiv: ru-196401.29116

This paper studies the size of defects of meromorphic functions in the plane in the sense of Nevanlinna theory, focusing on the supremum of the sum of square roots of positive deficiencies among functions of given lower order. Building on a theorem of Fuchs, the argument proves a new estimate for th…

Local criterion for the existence of wave operators

Unknown
1964 SovietRxiv: ru-196401.29088

This paper develops a local criterion for the existence of wave operators in abstract scattering theory for pairs of self-adjoint operators, defining strong and weak wave operators relative to a bounded Borel subset of the spectrum. It separates conditions ensuring weak existence, isometry, and comp…

Estimation of the Field in the Shadow Region during Diffraction of a Cylindrical Wave by a Bounded Convex Cylinder

Unknown
1964 SovietRxiv: ru-196401.28983

The paper studies high-frequency asymptotics for the exterior Neumann problem for the Helmholtz equation describing diffraction of a cylindrical wave by a smooth finite convex cylinder, with attention to the geometrical shadow region. It proves an upper bound for the field of order k^{-1/2} exp[-c k…

On the maximal boundary property of functions possessing integral representations of a certain type

I. B. SIMONENKO
1964 SovietRxiv: ru-196401.28625

This paper generalizes M. Riesz’s maximal boundary theorem for Hardy class functions to functions in a domain that admit integral representations over a smooth boundary with kernels satisfying boundedness, regularity, and off-diagonal control conditions. Using ideas associated with Calderon and Zygm…

On the density and quasi-Riemann hypotheses

Unknown
1964 SovietRxiv: ru-196401.28263

The paper studies the distribution of zeros of the Riemann zeta function and Dirichlet L-series near the line Re s = 1 by refining Linnik’s method of constructing sums that are large at zeros. Using estimates of I. M. Vinogradov, it partitions zeros of zeta up to height T into logarithmically many c…

On the Reduction of the Hilbert Problem for a Multiply Connected Domain to the Hilbert Problem with a Rational Coefficient

E. I. Zverovich
1964 SovietRxiv: ru-196401.26894

This paper studies the homogeneous Hilbert boundary value problem for a finite multiply connected planar domain and addresses its reduction to a Hilbert problem with a rational coefficient. Using harmonic measures, their conjugates on the covering surface, and solvability conditions for boundary rea…

ON THE REPRESENTATION OF CONTINUOUS AND DIFFERENTIABLE FUNCTIONS BY FOURIER SERIES IN LEGENDRE POLYNOMIALS

Unknown
1964 SovietRxiv: ru-196401.26423

This paper studies uniform convergence and error estimates for Fourier expansions of continuous and differentiable functions in orthonormal Legendre polynomials on the interval [-1,1]. Using a strengthened Jackson approximation theorem due to Timan, estimates for Legendre polynomial kernels, and the…

Construction of Envelopes of Holomorphy for Semitube Domains

Unknown
1964 SovietRxiv: ru-196401.26327

This note studies envelopes of holomorphy for semitube domains in several complex variables, extending earlier work that treated the case of one complex base variable. It defines locally normal semitube domains and proves that the envelope of holomorphy of any semitube domain is itself a locally nor…

Partial Multiplication Operations in Vector Structures

A. I. VEKSLER
1964 SovietRxiv: ru-196401.25797

This paper studies partial and full multiplication operations in ordered vector structures, focusing on when such operations can be represented as ordinary multiplication of continuous functions on the canonical space. It formulates axioms for partial multiplication, compares additional conditions u…

On Riemann Integration in Constructive Analysis

Unknown
1964 SovietRxiv: ru-196401.25213

The paper studies Riemann integration within constructive analysis, using normal algorithms and constructive functions on the unit segment. It defines integral partitions, integral sums, regulators of integrability, and the Riemann integral constructively, then proves several nonexistence results: i…

On the System of Canonical Open (Closed) Sets

Unknown
1964 SovietRxiv: ru-196401.25204

This note characterizes Hausdorff spaces whose Boolean structures of canonical open, equivalently canonical closed, sets are isomorphic to a given complete Boolean structure. It first records that dense extensions preserve these structures and proves that closed, irreducible mappings satisfying a ne…

Correlation Functions of a Gaussian Markov Process

Unknown
1964 SovietRxiv: ru-196401.24748

This paper characterizes the matrix correlation functions of a two-dimensional stationary, centered, normalized, nondegenerate Gaussian Markov process. Starting from positivity conditions for covariance matrices and the functional equations implied by the Markov property, the author reduces the prob…

On the Features of Taylor–Dirichlet Series

Unknown
1964 SovietRxiv: ru-196401.24599

This paper studies the location of singularities for Taylor-Dirichlet series of the form involving powers of the variable multiplied by exponential terms, under finite upper density conditions for the exponents counted with multiplicity. It introduces a condensation index adapted to multiplicities a…

Smooth Structures on Manifolds with Boundary

Unknown
1964 SovietRxiv: ru-196401.24378

This paper studies the classification of simply connected smooth manifolds with simply connected boundary, in dimensions greater than five with specified exceptions, that are homotopy equivalent to a fixed manifold and have equivalent stable normal bundles. Using Thom spaces, relative homotopy class…

Free Product of Associative Calculi with an Amalgamated Subalphabet and Some Related Questions

Ya. Ya. Sedol
1964 SovietRxiv: ru-196401.24336

The paper studies free products of associative calculi with an amalgamated subalphabet under group and isomorphism conditions, proving embedding and intersection properties for words belonging to the factor alphabets. Its main method introduces a combinatorial “analysis” of words using auxiliary let…

Correspondences over a quasi-exact category

Unknown
1964 SovietRxiv: ru-196401.24104

This note addresses the reconstruction of a category of correspondences from an arbitrary quasi-exact category, complementing earlier axiomatic work on correspondences over Abelian categories. It recalls the notions of an I-category, proper mappings, projections, injections, and quasi-exactness, the…

Quasi-nilpotent groups

Unknown
1964 SovietRxiv: ru-196401.24044

The paper introduces quasi-nilpotent groups, defined as groups in which every finite set of elements generates a subinvariant subgroup, and studies their position among generalized nilpotent groups. It establishes closure properties, constructs the quasi-nilpotent radical as the subgroup generated b…