Showing 50 of 5847 papers in Mathematics

On the Convergence of Orthogonal Series

V. F. GAPOSHKIN
1964 SovietRxiv: ru-196401.77196

This note studies sufficient coefficient conditions for almost everywhere convergence of orthogonal series, refining the classical Menshov and Rademacher logarithmic criterion. The author introduces a dyadic decomposition method whose subdivision points depend on a functional of the coefficients, yi…

Embedding theorems for some classes of abstract functions

A. H. Gudiev
1964 SovietRxiv: ru-196401.77188

The paper develops embedding theorems for mixed norm and weighted classes of abstract functions obtained by viewing functions on Euclidean space as functions of separate vector variables. It defines analogues of Sobolev, weighted Sobolev, and Besov type spaces with two integrability exponents, inclu…

On the existence of subgroups in a finite nonsolvable group

Ya. G. Berkovich
1964 SovietRxiv: ru-196401.76151

This paper studies how restrictions on solvable, noninvariant, Hall, and maximal subgroups constrain the structure of finite nonsolvable groups. It introduces and uses variants of subgroup types \(S\), \(B\), \(C\), \(p\)-decomposability, and a measure of quasinvariance for maximal chains, together …

On the limiting distribution of a certain class of functionals of a sequence of sums of independent random variables

Unknown
1964 SovietRxiv: ru-196401.75920

The paper studies limiting distributions for double-sum functionals of normalized partial sums of independent identically distributed random variables with mean zero and unit variance. Extending results of Skorokhod on one-dimensional functionals, it gives sufficient conditions on a sequence of nonn…

On the absolute convergence of the series of Fourier coefficients

1. The well-known theorem of Bernstein asserts:
1964 SovietRxiv: ru-196401.75898

This note studies the sharpness of Bernstein-type criteria for absolute convergence of Fourier coefficients in arbitrary complete orthonormal systems. Using a factorization argument through the coefficient map into l1, the synthesis map into L2, and multiplier operators, together with the theorem of…

On Stable Methods for Summing Fourier Series

Corresponding Member of the Academy of Sciences of the USSR A. N. TIKHONOV
1964 SovietRxiv: ru-196401.75751

The paper studies the stable recovery of a function value from approximate Fourier coefficients in an orthonormal system of eigenfunctions for a second order boundary value problem. Using Tikhonov regularization, it replaces ordinary Fourier summation, which is unstable under errors in the l2 metric…

On Some Completeness Criteria for the System of Root Vectors of a Linear Operator and Summability of Series with Respect to This System

Unknown
1964 SovietRxiv: ru-196401.75297

This note develops criteria for completeness of systems of root vectors of compact-related linear operators in Banach spaces and for Abel-type summability of expansions with respect to these systems. It proves completeness theorems under nuclearity, approximation-number, resolvent, numerical-range, …

Proof of the Existence of Analytic Functions of Several Variables Not Representable by Linear Superpositions of Continuously Differentiable Functions of Fewer Variables

Unknown
1964 SovietRxiv: ru-196401.75044

The paper proves an existence theorem for bounded analytic functions of two complex variables, real on the real plane, that cannot be represented on a given planar domain as a finite linear superposition of continuous one-variable functions composed with prescribed continuously differentiable functi…

ON SOME PERTURBATIONS OF A CLOSED LINEAR OPERATOR

Unknown
1964 SovietRxiv: ru-196401.74744

The paper studies perturbations of a closed linear operator in a Banach space by bounded operators drawn from a commutative Banach algebra that commute with it. It first proves algebraic stabilization criteria for the intersections of kernels with iterated ranges, showing in particular that stabiliz…

The solution of certain systems of equations in words

Unknown
1964 SovietRxiv: ru-196401.74182

The paper studies systems of equations in words over a fixed alphabet, with variables ranging over words, and addresses Markov’s problem of recognizing whether such a system has a solution. It introduces a formal class of terms built from words, powers, and recursively defined functions, then states…

On the Number-Theoretic Basis of Probabilistic Number Theory

M. B. BARBAN, A. I. VINOGRADOV
1964 SovietRxiv: ru-196401.74082

This note studies estimates underlying probabilistic number theory, especially the second fundamental lemma concerning integers whose component composed of small prime powers exceeds a given bound. Using earlier sieve estimates, the authors derive a sharper bound for this counting function, with dec…

On the distribution of prime numbers in short progressions $\operatorname{mod}p^n$

M. B. BARBAN, Corresponding Member of the Academy of Sciences of the USSR Yu. V. LINNIK, N. G. CHUDAKOV
1964 SovietRxiv: ru-196401.73593

The paper studies the distribution of prime numbers in arithmetic progressions modulo powers of a fixed prime, \(D=p^n\), a case where sharper results are sought than for general moduli. It proves that, for \(x \gg D^{8/3+\varepsilon}\), primes are asymptotically equidistributed among reduced residu…

On the Applicability of the Limit Theorem of Order $p>0$ to a Nonhomogeneous Markov Chain with Two States

An inhomogeneous Markov chain is considered in the form of a sequence of series of random variables
1964 SovietRxiv: ru-196401.73418

The paper studies sums of binary random variables forming an inhomogeneous two state Markov chain and asks when a central limit theorem together with convergence of absolute moments of order p is applicable. It introduces quantities describing products of transition differences and variances, then f…

Lower Bounds by the Sieve Method in Algebraic Number Fields

Unknown
1964 SovietRxiv: ru-196401.73319

The paper develops a modification of the sieve method that extends lower-bound results from the rational integers to arbitrary algebraic number fields, overcoming limitations caused by the weaker known zero-free region for Dedekind zeta-functions. The argument uses a zero-density estimate for zeros …

Continua with the fixed point property

Unknown
1964 SovietRxiv: ru-196401.72733

This paper studies fixed point properties of one-dimensional acyclic continua, in connection with a problem of P. S. Aleksandrov concerning arbitrary continuous self-maps. It proves that a continuum has the fixed-point property if it can be epsilon-mapped onto finite trees so that inverse images of …

A difference method for solving Stefan-type problems for a quasilinear parabolic equation with discontinuous coefficients

Unknown
1964 SovietRxiv: ru-196401.72033

This paper studies two-phase and one-phase Stefan-type free-boundary problems for quasilinear parabolic equations with discontinuous spatial coefficients and nonlinear boundary conditions, including radially symmetric cylindrical and spherical cases after transformation. It constructs an implicit fi…

A universal bicompactum of given weight and given dimension

Unknown
1964 SovietRxiv: ru-196401.71976

The paper proves the existence, for every infinite cardinal weight and every natural dimension n, of a compact Hausdorff space of that weight and dimension n that contains a topological image of every completely regular space of weight at most that cardinal and dimension at most n. The argument cons…

Estimates for the Spectrum of Normal Operators

Unknown
1964 SovietRxiv: ru-196401.71972

This paper extends estimates for eigenvalues obtained from a quotient of a trial vector and its image to arbitrary normal operators in Hilbert spaces of functions or sequences. It proves that if the pointwise ratio of Af to f has its values in a disk, exterior disk, or half-plane on the Riemann sphe…

Open mappings of proximity spaces

Unknown
1964 SovietRxiv: ru-196401.71366

This paper introduces and studies several classes of mappings for proximity spaces intended to parallel open, closed, and preclosed mappings in topology. It defines proximally open, weakly open, regular, almost regular, and almost factor mappings, establishes characterizations in terms of closeness,…

On the Classical Solvability of Diffraction Problems for Equations of Elliptic and Parabolic Types

O. A. Ladyzhenskaya, V. Ya. Rivkind, N. N. Ural’tseva
1964 SovietRxiv: ru-196401.71334

The paper studies classical solvability of diffraction problems for second order elliptic and parabolic equations with coefficients having jump discontinuities across interfaces between media. It formulates model boundary and initial boundary value problems with continuity of the solution and conorm…

Isotopy of

Unknown
1964 SovietRxiv: ru-196401.70092

This paper outlines a method of local rearrangement of homeomorphisms of Euclidean space and applies it to isotopy problems for locally flat embeddings. For integers satisfying k less than two thirds of n minus 1, it proves that every homeomorphism of n-dimensional Euclidean space factors into a sta…

On Non-Self-Adjoint Operators Generated by Jacobi Matrices

Unknown
1964 SovietRxiv: ru-196401.68864

This note studies nonselfadjoint extensions of symmetric operators with defect indices one and one generated by Jacobi matrices in a separable Hilbert space. Using the associated orthogonal polynomials and their polynomial kernel, it derives the characteristic function of the extension A_theta and i…

General boundary value problems for elliptic equations in a domain whose boundary consists of manifolds of different dimensions

Unknown
1964 SovietRxiv: ru-196401.68722

This paper studies general boundary value problems for elliptic differential operators in bounded domains whose boundary is a union of smooth manifolds of different dimensions, extending earlier work on polyharmonic Dirichlet problems. It formulates Sobolev space settings and ellipticity conditions,…

On Conditions for the Analyticity of the Scattering Matrix

A. G. RAMM
1964 SovietRxiv: ru-196401.68202

This paper studies inverse conditions for the analyticity of the Jost function associated with a one-dimensional Schrödinger scattering problem on the half-line. It proves that if the Jost function is entire of growth order at most one and its deviation from 1 is square-integrable, under the stated …

On zeros of the gradient of a harmonic function

Unknown
1964 SovietRxiv: ru-196401.67534

This note studies the local and compact structure of the set of critical points of a nonconstant harmonic function in a three-dimensional domain. Using standard results on real-analytic sets, including decomposition into irreducible components and the local behavior of one-dimensional analytic sets,…

On saturation classes in the theory of singular integrals

Unknown
1964 SovietRxiv: ru-196401.66651

The paper studies saturation phenomena for approximation of continuous periodic functions by positive even singular integrals and by iterated combinations of such integrals. Using Fourier multiplier representations and the Turetskii, Kharshiladze saturation criterion, it proves that under standard m…

On Some Stability Properties of Bases

Unknown
1964 SovietRxiv: ru-196401.66595

This paper studies stability criteria for bases in separable Banach spaces and Hilbert spaces under perturbations weaker than classical norm summability conditions. It first proves equivalent characterizations of unconditional convergence, including regular convergence uniform over the dual unit bal…

On the Description of Extensions of Positive Definite Kernels

M. L. GORBACHUK
1964 SovietRxiv: ru-196401.66167

This note studies positive definite kernels with values in a Hilbert space and their extensions under commutation conditions with ordinary differential expressions. It proves a representation theorem expressing such operator kernels through fundamental solutions of differential equations and a nonne…

On Some Inequalities for Functions from Weighted Classes and Boundary Value Problems with Strong Degeneracy on the Boundary

Unknown
1964 SovietRxiv: ru-196401.66147

This paper establishes Poincare type inequalities for functions whose highest derivatives are integrable with powers of the distance to the boundary as weights. Using one dimensional estimates, bridge coverings of smooth bounded domains, and weighted Sobolev classes, the authors derive inequalities …