SovietRxiv · Open Access in English
Rediscovering the Soviet scientific archive, in English
25357 full-text translations 14926 English PDFs 22539 abstracts
Showing 50 of 5847 papers in Mathematics
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…
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…
This paper studies the distribution of zeros of solutions of real linear ordinary differential equations on a finite interval, introducing classes of operators defined by the absence of solutions with prescribed multiple zeros at two points. It develops comparison and nonoscillation results for self…
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 …
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…
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…
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…
This note studies stability of the Bubnov-Galerkin method for nonstationary operator equations in a Hilbert space, including parabolic, hyperbolic, and more general equations with first and second time derivatives. The approximation is formed from a prescribed coordinate system in a Hilbert space as…
This paper studies Cauchy-type problems for first-order hyperbolic systems whose initial data are prescribed on a line of degeneration, a setting in which the usual formulation is generally not well posed. Using modified boundary conditions and transformations to characteristic integral equations, i…
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, …
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…
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 paper studies the Cauchy problem for the three-dimensional Laplace equation after transforming it to complex variables, with holomorphic initial data prescribed on the plane zeta equals zero. It derives series solutions, analyzes their convergence, and gives an integral representation over the s…
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…
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…
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…
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…
The paper derives expansion formulas for Kampé de Fériet double hypergeometric functions of higher order, a class that includes the Appell functions as special cases. Using direct rearrangement of convergent double series rather than symbolic differential operators, it establishes two general theore…
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 …
The paper studies convergence and uniqueness constants for a broad class of interpolation problems that includes the Abel-Goncharov, Pommiez, and generalized gamma problems, in spaces of analytic or entire functions defined by coefficient growth. Using estimates for interpolation polynomials, recurr…
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 …
The paper studies automorphic solutions on a fundamental polygon of a Fuchsian group for a generalized analytic equation of the form ∂U/∂z̄ = A(z)Ū, allowing prescribed poles and discontinuous coefficients. Using the standard factorization of meromorphic generalized analytic functions, it reduces a…
The paper studies the inclusion structure of closed classes of functions in countably valued logic under closure by superposition, with particular attention to classes of finite height. It defines height for closed classes and constructs, using specially encoded unary functions indexed by infinite s…
This paper studies orderedness of characteristic matrix functions associated with simple dissipative Volterra operators whose imaginary component is two-dimensional, a property equivalent to unicellularity of the operator. Using multiplicative Stieltjes integral representations and canonical factori…
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…
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…
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…
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,…
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…
This paper studies when a connected semisimple algebraic group over a number field splits after completion at prime divisors of the ground field. Using the correspondence between forms of a split semisimple Lie algebra and Galois cohomology classes in the automorphism group, the argument reduces loc…
This note studies the asymptotic behavior of solutions to homogeneous systems of integral equations arising in mathematical physics, including Wiener Hopf systems, paired integral equations, and transposed paired systems. Using Fourier transform methods and spectral conditions on exponentially decay…
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…
The paper studies centro-projective connections on differentiable manifolds with an almost complex structure, focusing on connections conjugate with respect to a copuncture and their relation to associated affine connections. It defines conjugate and symmetrically conjugate centro-projective connect…
The paper studies the first boundary-value problem for a fourth-order elliptic equation that degenerates on part of the boundary of a bounded domain, where the limiting equation has a quasi-parabolic character. It shows that the correct formulation of the boundary conditions depends on the sign of t…
The paper develops a consequence of K. Fan’s lemma that extends Tikhonov’s fixed point principle in locally convex separable topological vector spaces. It proves that for a continuous mapping on a convex compact set, affine in one variable and satisfying a solvability condition, there is a point sat…
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…
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,…
This note presents integral representation results for several classes of analytic functions, extending Paley-Wiener type theorems for entire functions of finite order and normal type. Using Mittag-Leffler type kernels, it gives parametric representations and uniqueness formulas for entire functions…
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 …
This note studies why optimal strategies in certain antagonistic games with random mediation or asymmetric information can often be chosen without additional randomization. It analyzes two models: a bluffing game in which one player observes a continuously distributed parameter affecting payoffs, an…
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,…
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…
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…
This paper studies relative stability in probability for sums of nonnegative random variables whose dependence is governed by a Markov chain. Using Dobrushin-type coefficients of ergodicity, it gives sufficient conditions, formulated through truncated marginal distributions and normalizing constants…
The paper studies rational Chebyshev approximation formulated as the minimization, over a bounded convex domain with smooth convex constraints, of the maximum of a finite system of fractional linear functions. Although the objective is not convex, the authors argue that it has no local minima in the…
The paper studies the existence, uniqueness, stability, and instability of time-periodic nonnegative solutions for a quasilinear parabolic equation on a bounded domain with homogeneous boundary conditions and a periodic nonlinearity. The argument reformulates the initial-boundary value problem as an…
The paper introduces generalized characteristic numbers for trajectories in a punctured neighborhood of an equilibrium, defined through a scalar level function and a distance-like function satisfying monotonicity and subadditivity conditions. It applies these numbers to autonomous differential syste…
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…
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 …
The paper studies the probability that a Markov random point in Euclidean space enters a small moving neighborhood of a time-dependent differentiable submanifold. Using the Kolmogorov equation for the transition density, it constructs local coordinate frames adapted to the diffusion operator and to …
