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 analogues of the Weierstrass canonical product for entire functions of several complex variables when only a specially chosen codimension-one part of the zero set is specified. It defines averaged zero-counting functions on radial and cylindrical sections of the analytic zero set a…
This paper studies inverse boundary value problems in which coefficients of a parabolic equation and of an ordinary differential equation are unknown, with the spatial dependence of one coefficient assumed piecewise constant. Using additional data prescribed at finitely many points and boundary flux…
The paper studies one-dimensional multiphase Stefan-type problems with several moving internal and external fronts governed by nonlinear parabolic equations and front conditions. It applies a front-straightening change of variables that maps each moving phase interval to a fixed strip, then uses suc…
This note studies metrizability questions for finally compact and related topological spaces with point-countable bases. Its main theorem proves that a finally compact p-space with a point-countable base must have a countable base and is therefore metrizable, using perfect mappings onto second-count…
The paper studies a discontinuous linear conjugation boundary value problem for analytic functions in Hardy classes on a closed Riemann surface with Lyapunov contours and measurable data. It develops an analogue of Schwarz’s alternating method to prove a harmonic extension theorem, then applies it t…
This note develops properties of constructive generalized functions, continuing the author’s earlier definition of a constructive analogue of classical distributions. It introduces equality on intervals, carriers and bounded carriers, limits of sequences and parameter-dependent families, linear chan…
This paper studies solvability of first and second order Cauchy problems for abstract parabolic equations in a Banach space with time dependent, generally unbounded operators whose domains may vary with time. Under resolvent estimates and Hölder type continuity assumptions on the operator coefficien…
This paper studies non-self-intersecting curvilinear rays on closed surfaces, understood through their lifts to the universal covering surface. It proves that any such lifted ray which goes to infinity has an asymptotic direction, treating orientable surfaces of negative Euler characteristic via the…
This paper extends earlier results on second order elliptic equations that degenerate on a closed subset of the boundary to bounded domains with arbitrary smooth boundary. It formulates Dirichlet and oblique derivative boundary value problems in which the ellipticity may fail on separated boundary p…
The problem of approximating, on a finite time interval, the solutions $x(t)$ of an $n$-dimensional system of linear differential equations \begin{equation} dx(t)/dt=\sum_{i=1}^n A_i(t)x_i(t-h_i(t)) \label{1} \end{equation} with variable delays $0\le h_i(t)\le h$ is considered. It is shown that the …
This paper develops an operational approach for obtaining integral characteristics of nonstationary diffusion or heat transport in active, possibly multilayer media without explicitly inverting Laplace transforms. It considers processes with linear conversion or source terms and shows that quantitie…
This paper extends Korovkin-type convergence theorems for sequences of linear positive operators by replacing uniform convergence with convergence in the Hausdorff distance between completed graphs of functions. It introduces the notion of local monotonicity through a modulus of nonmonotonicity and …
This note extends aspects of Jordan theory to a class of bounded linear operators in separable Hilbert space whose spectrum is concentrated at zero, whose imaginary part is nonnegative, and whose imaginary component has finite trace. Using Brodskii’s notion of a single-block operator and a quasidire…
This note studies a one-dimensional analogue of a second-order elliptic equation whose leading coefficient vanishes at the boundary, focusing on smoothness of bounded solutions up to the degeneracy point. The equation is reduced to Volterra integral equations, and properties of the associated integr…
The paper develops a realization of infinite-dimensional representations of the rotation group, or equivalently SU(2) locally, with arbitrary complex weight in spaces of single-valued entire functions, avoiding earlier realizations by multivalued analytic functions with branch singularities. Startin…
The content of the article is determined by the decisive role of a special exponent in the study of solutions to differential equations. The main result is contained in Theorem 1: If the operator $A(t)$ in equation \begin{equation} \frac{dx}{dt}=A(t)x\tag{1} \label{1} \end{equation} is such that for…
This paper studies an elliptic boundary value problem in a bounded three-dimensional domain with an oblique derivative condition that degenerates along a finite set of boundary curves where the oblique field becomes tangent. The boundary curves are classified by the direction of the field on their t…
Linearly independent systems \begin{equation} \{\ln r(x_i,y)\},\quad\biggl\{\frac{\partial}{\partial n_y}\ln r(x_i,y)\biggr\}\quad(i=1,2,\dots), \label{1} \end{equation} are considered, where $x_i$ are uniformly distributed on the circle $S_1$, and $y \in S$; here, $S$ and $S_1$ are concentric circl…
This paper studies existence and uniqueness for nonlinear Hammerstein integral equations with symmetric matrix kernels in general ideal Banach spaces of vector functions. The authors reduce solvability questions to properties of the associated linear integral operator and the superposition operator,…
The paper studies boundedness criteria for Nemytskii operators and applies them to Sobolev’s problem of characterizing coefficient functions satisfying a condition called T-invariance for quasilinear hyperbolic equations. It first proves that a Carathéodory function A(x,y) defines a bounded operator…
This note studies topological invariants of noncompact Lie groups that become visible when principal bundles are allowed to have Hausdorff, possibly nonparacompact, bases, rather than only CW-complex bases. It constructs universal spaces for such bundles and proves that natural assignments from prin…
A regular solution of the equation \begin{equation} L_nL_{n-1}\dotsb L_1u=0, \label{1} \end{equation} is considered, where $$L_i=A_i\frac{\partial^2}{\partial x^2}+2B_i\frac{\partial^2}{\partial x\partial y}+C_i\frac{\partial^2}{\partial y^2}+D_i\frac{\partial}{\partial x}+E_i\frac{\partial}{\partia…
The paper studies Dirichlet problems for second order elliptic systems written in complex form, focusing on cases where the standard problem is not Noetherian unless suitable terms involving the conjugate unknown are present. It derives integral representations of solutions through holomorphic funct…
The paper studies solvability of nonlinear operator equations of the form K1K2(u) + K3(u) = h in reflexive separable Banach spaces, motivated by boundary value problems for quasilinear elliptic and parabolic equations and related integro-differential equations. Using a Galerkin approximation scheme …
The paper compares uniform approximation of analytic functions on the closed unit disk by polynomials and by rational functions of bounded degree. Using a Hahn Banach best approximation criterion, the authors derive lower bounds for rational approximation of certain lacunary power series and show ca…
This note studies radial boundary values of meromorphic functions in the generalized Nevanlinna classes defined by a bounded alpha-characteristic, focusing on the case minus one less than alpha less than zero. Using the parametric representation of these classes, generalized Blaschke products, estim…
The paper studies equivalences between a branching property for a strongly inaccessible cardinal and compactness or cardinality conditions in general topology. It reviews earlier equivalences involving branching systems, ordered compacta, and T^sigma products, then proves that the branching property…
We consider the problem of finding a solution to the following system of equations: $$\frac{\partial u^{(1)}}{\partial t}=\sum_{l=0}^2C_{0l}^{(1)}(x)\frac{\partial^lu^{(1)}}{\partial x^l}+f^{(1)}(x,t),\quad x\in(a_1,b_1),\quad t\in(0,T),$$ $$\frac{\partial^2 u^{(2)}}{\partial t^2}=\sum_{\substack{{k…
This paper studies best uniform approximation on the real line of uniformly continuous real functions by entire functions of finite exponential type, in terms of a prescribed modulus of continuity. Using properties of a nonlinear supremum operator and a theorem on approximation of Lipschitz function…
This paper extends Calderón’s construction of intermediate Banach structures from measurable function spaces to broader semiordered spaces, focusing on conjugate and dual spaces. It proves that, for suitable \(b\)-complete \(KN\)-spaces \(X_1\) and \(X_2\), the conjugate of \(X_1^{1-s}X_2^s\) coinci…
The paper considers a necessary and sufficient condition for the validity of a theorem analogous to S. A. Chaplygin's theorem on differential inequalities for an elliptic difference equation. Effective estimates of the domain of applicability of the mentioned theorem to difference and differential e…
This paper studies the uniform approximation of functions from a generalized Lipschitz class by positive linear operators generated from an orthonormal system with respect to a monotone weight. It derives an upper estimate for the pointwise maximal deviation of such operators in terms of the modulus…
This paper studies uniform convergence on the full interval of Fourier series in Jacobi polynomials for continuous functions of bounded variation. Using estimates for the Jacobi kernel, integral bounds for partial sum kernels, asymptotic formulas, and mean value arguments, it proves boundedness of c…
The paper introduces a new definition of an integral of Temlyakov type for bicircular convex domains of class T in two complex variables, allowing densities given on a product parameter set rather than only on the boundary. It establishes conditions under which these integrals are holomorphic in the…
The paper studies an inhomogeneous singular Cauchy problem for a linear differential operator independent of the singular variable, comparing its solutions with those of the corresponding homogeneous parameter case. It derives series expansions, connection formulas, addition theorems, and integral r…
This paper develops an analogue of the Andronov-Witt stability theorem for autonomous ordinary differential equations with a bounded, not necessarily periodic, reference solution. It introduces standard and completely bounded solutions for associated linear systems, proves a representation lemma for…
This paper studies bounded solutions of second-order elliptic equations in unbounded domains, focusing on the structure of the boundary at infinity when different limiting values may occur along different paths. Using the diffusion process associated with the elliptic operator, the author gives cond…
The paper studies uniqueness and solvability of multipoint boundary value problems for linear ordinary differential equations of order n with continuous real coefficients. It derives sharper sufficient estimates for the length of the interval of unique solvability than earlier bounds of Vallée-Pouss…
This note addresses Shimura’s conjecture on the rationality of the local Hecke series for the Siegel modular group, specializing to genus 3. The argument identifies the relevant Hecke ring with a subring of a local convolution algebra, expresses the Fourier transform of the Hecke series as a zeta fu…
This paper studies periodic solutions of differential equations in a Banach space whose right-hand side switches between two values according to hysteresis thresholds defined by a continuous linear functional. Using semigroup assumptions on the linear operator and spectral separation by a simple dom…
This paper develops a duality theory for concave-convex games defined on products of convex subsets of finite-dimensional spaces, using conjugate sets associated with hypographs and epigraphs of a closed kernel. It constructs conjugate functions through successive optimization in the two variables a…
