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 paper establishes a priori estimates for generalized solutions and subsolutions of second order elliptic and parabolic equations in divergence form with measurable uniformly elliptic leading coefficients and lower order terms in Lebesgue spaces. Using integral inequalities and iteration methods…
The paper introduces a special case of local topological products, formed by replacing selected fibers over open subsets of a base space by two-point fibers while collapsing fibers elsewhere, and extends the construction to arbitrary systems of open sets via inverse spectra. It establishes preservat…
The paper develops a theory of absolutes for arbitrary Hausdorff spaces with respect to irreducible theta-continuous closed mappings. It constructs, for each Hausdorff space, a hyperabsolute as the space of maximal centered systems of open sets and identifies the subspace of proper ends as the absol…
This note studies infinite-dimensional linear groups that satisfy finiteness conditions making them close to finite-dimensional linear groups, especially local versions of admissible finite-dimensional representation and finite-dimensional generated operator algebra. It introduces and compares sever…
The note studies uniqueness for entire functions represented by absolutely convergent Dirichlet series with positive real exponents and bounded on the real axis. For exponent sequences satisfying \(\lambda_n \sim c n^{1/q}\), \(1<q<2\), it proves that if the majorant \(M_F(x)=\sum |a_n|e^{\lambda_n …
The paper describes the ideal structure of the semigroup of endomorphisms of a free algebra in a primitive class of universal algebras. It identifies the complete lattice of left ideals with a lattice of downward closed families of subalgebras generated by no more than the rank of the free algebra, …
This note studies general boundary value problems for parabolic systems, first in a half space with constant coefficients and then for systems with variable coefficients and boundary conditions in one spatial coordinate. It reformulates the solvability condition through an auxiliary ordinary differe…
The paper studies a class of functions of several real variables with mixed generalized derivatives satisfying Hölder-type difference estimates in Lp. It proves that every function in this class can be expanded as a series of entire functions of exponential type with coordinatewise degree bounds and…
This paper studies traces of functions in the fractional differentiability spaces \(L_p^r(E_n)\) on lower-dimensional hyperplanes and relates them to Besov-type spaces \(B_p^s\). Using potential representations, metaharmonic extensions, weighted integral estimates, and inequalities of Hardy, Littlew…
This note studies recurrent sequences modulo a prime ideal in an algebraic number field, allowing coefficients that are periodic rather than constant. It relates such recurrences to products of companion-type nonsingular matrices over the finite residue field, using properties of the general linear …
This paper studies double quotient spaces of the idèle group of an algebraic group over a number field by realizing them as first cohomology sets of sheaves of local units on the space of finite prime divisors. Using an approximation theorem for connected algebraic groups, it identifies \(H^1\) of t…
This note refines Bernstein-type inequalities for polynomials bounded on an interval by incorporating restrictions on the location of their zeros. Using elementary estimates on products over the zeros, it derives upper and lower bounds relating the maximum modulus of a polynomial on intervals of the…
This paper studies gradient methods for finding a local minimum of a nonlinear functional on a real Hilbert space subject to finitely many linear equality constraints. It formulates the constrained steepest descent as a projected gradient differential equation on the constraint plane and proves conv…
This note studies constructive properties of duplexes, represented by rational Cauchy sequences together with regulators of self-convergence, and examines whether minimal regulators can be uniformly obtained. It proves that no algorithm can transform an arbitrary duplex into a minimal regulator for …
This paper formulates an optimal control variational problem in which the performance functional and endpoint constraints depend not only on initial and terminal states but also on coordinate values at prescribed intermediate times. Using Lagrange multipliers and comparison curves, it derives first-…
This note studies the index of systems of multidimensional singular integral equations on manifolds without boundary, under standard smoothness and nonsingularity assumptions on the symbolic matrix. It argues that, when the order of the system exceeds the manifold dimension, computation of the index…
This note studies the partially ordered set of matrix norms on the ring of real square matrices of fixed order, ordered by pointwise domination, and asks about the structure of its maximal chains. Using Zorn’s lemma to ensure maximal chains, the argument proves two auxiliary facts: any nonzero pseud…
This paper studies the approximate solution of nonlinear operator equations in Banach spaces by the method of tangent hyperbolas and a related modified iteration that fixes certain derivatives at the initial point. Using the majorant principle, it establishes convergence theorems under assumptions o…
This paper studies a mixed boundary value problem for a first order quasilinear hyperbolic system in a strip, with nonlocal boundary conditions involving time integrals. A finite difference grid scheme is constructed, and under Lipschitz and compatibility assumptions the paper establishes local exis…
This paper studies biharmonic functions in the unit disk satisfying a zero normal derivative condition on the boundary, with emphasis on estimating how far interior values can deviate from their boundary values. It proves general inequalities in terms of the boundary modulus of smoothness or continu…
This paper gives criteria for almost everywhere absolute Cesàro summability of multiple Fourier series of functions periodic in several variables. Extending earlier work on absolute convergence and summability, it formulates sufficient conditions involving only separate restrictions in each variable…
This note studies boundary value problems for four component vector functions holomorphic in a three dimensional ball, where holomorphicity is defined by an elliptic first order system with matrix differential operator. Using a complex form of the system and expansions in spherical functions, it ana…
The paper studies first-order systems of partial differential equations for two functions of two variables whose solution sets, interpreted as mappings of the plane, form groups under composition. It shows that, subject to the identity solution condition, this requirement is equivalent to Lie invari…
The paper studies finite groups that factor through or contain maximal subgroups satisfying a generalized decomposability condition relative to a set of primes. It extends questions about solubility and supersolubility of products of subgroups to the settings of Pi-separability, Pi-solubility, stron…
This paper studies finite systems of linear inequalities with real parameters over a real linear space, focusing on transformations called convolutions or collapses relative to a subspace. It characterizes such combinations through cones of nonnegative dependencies among the restricted linear functi…
This note studies extension problems for functions in anisotropic Nikol’skii type spaces defined by mixed smoothness conditions in the variables. It proves that functions, and more generally prescribed normal derivatives, belonging to the corresponding boundary class can be extended from a hyperplan…
This paper extends variational methods for operator equations in Hilbert space from the self-adjoint positive case to certain non-self-adjoint equations. It introduces an auxiliary operator B and uses the notions of B-symmetry and B-positivity to define B-extensions, a corresponding energy space, an…
The paper introduces a notion of Dini convergence for Moore Smith sequences in a prescribed family of real valued functions, defined by the existence of monotone squeezing sequences with a common pointwise limit. It shows that for systems of continuous functions this convergence implies local unifor…
This note studies completeness of exponential systems of the form {e^{λ_n z}} in closed horizontal strips, extending earlier results for open strips. It gives sufficient conditions, formulated through a decomposition of the exponent sequence and zeros of entire functions of exponential type, under w…
The note studies consistent estimation of the conditional expectation of an unknown random parameter given an observation in Robbins’ empirical Bayes scheme, when the prior distribution of the parameter is unknown. It proves a positive result for compact parameter sets and continuous sampling densit…
This paper studies special structural spaces associated with rings and special classes of prime rings, using the corresponding special radical and the topology on special ideals. It establishes criteria for bicompactness of the structural space, including finite generation conditions on ideals and a…
This paper studies generalized solutions of second order elliptic equations in divergence form with measurable coefficients that may degenerate, together with lower order drift terms satisfying integrability and sign conditions. Using Moser’s iteration method and weighted embedding estimates, it der…
The paper addresses whether an operator in Kühne’s class of bounded J-self-adjoint operators must be completely continuous when one of its powers is completely continuous. It constructs, in a Hilbert space with both positive and negative J-metric subspaces infinite-dimensional, a J-positive operator…
This note studies continuous dependence on initial data for the first boundary-value problem for a parabolic equation considered backward in time, a problem known to be ill posed in general. Under uniform boundedness assumptions on solutions, it derives quantitative stability estimates for the diffe…
This paper studies Urysohn integral operators acting on spaces of continuous vector functions over a bounded closed subset of finite-dimensional Euclidean space. It derives necessary conditions from boundedness and compactness, including weak continuity and integral boundedness and equicontinuity re…
This note studies spectral properties of bounded symmetric operators generated by higher order systems of differential equations of S. L. Sobolev type in Hilbert spaces of solenoidal vectors and associated function spaces. It defines the operators through elliptic boundary value problems with consta…
The paper constructs scales of Orlicz spaces by defining intermediate N-functions through geometric interpolation of inverse complementary functions, and studies their ordering, equivalence, and preservation of growth conditions such as the Delta2 condition. It proves that the resulting spaces are d…
The paper studies constructive characterization of classes of bounded continuous real-valued functions on an arbitrary separable metric space in terms of uniform approximation by functions satisfying a Bernstein-type Lipschitz inequality. It defines best approximations by such generalized entire fun…
The paper develops a steepest descent method for solving linear equations in Hilbert modules over a finite-dimensional complex K-space. It first formulates the necessary module structure, structural norm and product, regular operators, homogeneous operators, and positivity properties needed to trans…
The paper studies the remainder term in asymptotic formulas for weighted counts of integer points satisfying congruence conditions inside multidimensional ellipsoids defined by positive definite integral quadratic forms, with dimension greater than four. Using methods associated with Landau, Walfisz…
This paper studies regularizing properties of potentials associated with a general uniformly elliptic second-order equation in a bounded domain with sufficiently smooth boundary and coefficients. It proves that the direct value on the boundary of the double-layer potential, and the direct value of t…
This paper studies geodesic correspondences of semi-reducible Riemannian spaces with indefinite metric, extending earlier results for positive-definite Levi-Civita spaces and the class of spaces denoted V(K). Using the differential equations characterizing metrics with common geodesics, it analyzes …
This paper studies products of bases of analytic functions in arbitrary simply connected domains, extending earlier results that treated disks or simple unit bases. Using Faber polynomials and associated isomorphisms between disk spaces and spaces of functions analytic on domains bounded by Jordan c…
This paper extends a process of successive approximations for solving functional equations from fixed point equations to equations of the form Ax = 0 in semi-ordered spaces. It establishes convergence and uniqueness results for monotone Fréchet differentiable operators whose derivatives are bounded …
This paper addresses the finite axiomatizability of identities in many-valued logics, motivated by Lyndon’s positive result for two-valued logic and negative example for seven-valued logic. It constructs a closed class of functions in four-valued logic generated by a specified binary operation and s…
The paper studies non-self-adjoint boundary-value problems on the half-axis for a second-order differential expression with exponentially summable potential, including cases with spectral singularities where the associated Fourier transform is not uniquely invertible. It develops a functional calcul…
This paper develops and refines an iterative algorithm for the convex Chebyshev approximation problem, presented mainly for inconsistent systems of linear complex equations. At each step the method selects a descent direction from the active or nearly active maximal deviations, reducing its determin…
This note studies variants of representability of enumerable sets in generating bases, especially when strict representation is modified by partitions of words or by algorithms translating words between alphabets. It introduces notions such as strongly decidable bases, representation relative to pri…
This note proves conditions under which a condensation, understood as a one-to-one continuous mapping, onto Euclidean space must be a homeomorphism. The main theorem states that any condensation from a connected, locally bicompact paracompact space onto Euclidean space is a homeomorphism, with a str…
The paper extends Sobolev’s embedding theory for abstract additive set functions with values in a Banach space. It introduces Lipschitz-type classes for such functions on domains and on intersections with smooth manifolds, then derives kernel estimates from an integral representation of sufficiently…
