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 proves nonexistence results for linear polynomial operators that would approximate every function with error of the same order as the best trigonometric polynomial approximation. For continuous periodic functions, the argument shows that such an operator would imply a uniform bound of the …
This paper studies convergence of the method of averaging functional corrections for linear Fredholm integral equations of the second kind with square integrable real kernel and inhomogeneous term. It formulates the iterative scheme, estimates successive corrections in the \(L^2\) norm using Minkows…
This paper proposes a general functional series framework for deriving numerical formulas for ordinary differential equations, extending earlier approaches to broader classes of integration schemes. By expanding the series terms and matching coefficients with the Taylor expansion, the derivation of …
The paper studies binary additive representations involving primes, principally integers of the form n = p1 + p2^p3, where p1 and p3 are prime and p2 is a fixed prime. Using estimates based on the Brun-Schnirelmann sieve and an identity of Romanov, it derives an asymptotic formula for the number of …
The paper studies the Tricomi boundary value problem for a general Lavrent’ev-Bitsadze equation of mixed elliptic-hyperbolic type in a domain bounded by a curve in the elliptic half-plane and characteristics in the hyperbolic half-plane. It establishes uniqueness using maximum principles for general…
This paper supplies a proof scheme for previously derived formal asymptotic expansions of solutions to singularly perturbed systems of differential equations near a breakdown point, where the relevant Jacobian determinant vanishes. After reducing the system to a normal local form, the authors divide…
This paper studies the convergence of formal power series solutions for nonlinear Uryson integral equations with analytic nonlinearities and small parameters. It extends the theory of formal power series from numerical to functional coefficients and applies Lyapunov, Schmidt reduction to relate form…
This paper studies asymptotic behavior of solutions to boundary-value problems whose boundary data oscillate rapidly along time or boundary coordinates. Extending earlier work on elliptic equations, it treats parabolic equations, hyperbolic equations, elliptic operators with a small degenerating par…
This note addresses the weakened Burnside problem for groups with a fixed finite number of generators and prime exponent, reducing the question to a nilpotency problem for Lie rings of characteristic p satisfying an Engel condition. Using iterative constructions of special Lie elements and an analys…
This paper studies the distribution of divisor functions and values of primitive positive binary quadratic forms in arithmetic progressions, especially for moduli too large for existing estimates based on Kloosterman sums. It develops mean square, or dispersion, estimates showing that the expected a…
This note studies the distribution of nodes required for uniform convergence of S. N. Bernstein’s modified interpolation process on the interval \([-1,1]\), in contrast to the classical impossibility result for ordinary Lagrange interpolation on arbitrary continuous functions. It proves that if Bern…
The note studies the asymptotic behavior of solutions to systems of linear equations with infinite matrices whose entries vary smoothly with the indices. It first derives explicit formulas and limiting results for finite banded Toeplitz systems in terms of the zeros of an associated Laurent polynomi…
The paper develops embedding theorems for classes of functions of several variables whose partial derivatives with respect to different variables are measured in possibly different Lebesgue metrics. It defines anisotropic classes with separate smoothness orders and exponents, then proves conditions …
The note presents a standard construction that associates to each pair of isometric surfaces in elliptic or Lobachevsky space a pair of isometric surfaces in three-dimensional Euclidean space, and conversely constructs corresponding pairs in spaces of constant curvature from Euclidean isometric surf…
This paper studies Temlyakov integral representations for analytic functions of two complex variables in bicircular domains with specified convexity properties. It establishes continuity and analyticity properties of Temlyakov integrals of the first kind under Hölder-type boundary assumptions, analy…
The paper studies second-order linear differential equations with periodic coefficients, focusing on bounds for Floquet multipliers when the coefficient is a generalized derivative \(p=q'\) with a fixed quadratic constraint on \(q\) and zero mean. It establishes sharp restrictions on which instabili…
This paper develops new estimates for rational trigonometric sums and applies them to problems concerning the Riemann zeta function and the distribution of prime numbers. Combining Vinogradov’s method with an approach that exploits the rational structure of the sums, it proves a strengthened bound f…
This paper studies when continuous complex functions on plane sets can be uniformly approximated by functions analytic in a neighborhood, using analytic capacity and harmonic capacity to measure the size of complements locally. It proves a basic approximation lemma that replaces Cauchy kernels by fu…
This paper constructs fundamental matrices of solutions for general linear systems that are parabolic in the sense of Petrovskii, extending earlier work on systems first order in time. Under boundedness, Hölder continuity, and related regularity assumptions on the coefficients, it establishes existe…
This note studies the relation between Chebyshev sets, defined by existence and uniqueness of best approximations, and convex sets in Banach spaces. It gives geometric criteria involving the unit sphere, especially strict convexity and absence of conical points, and proves that in a finite-dimension…
This paper studies boundary value problems for uniformly elliptic quasilinear first order systems in the plane, written in complex form with coefficients measurable in the independent variable and Lipschitz or controlled in the dependent variable. The boundary condition is reduced to a canonical for…
This paper studies best Chebyshev approximation of continuous functions on a compact set with values in an infinite-dimensional commutative Hilbert ring by generalized polynomials with coefficients in that ring. Using the decomposition of ring elements into orthogonal idempotents and an operator-fun…
The paper studies saturation classes for linear summation processes associated with Fourier expansions in spaces of periodic functions, including continuous functions and \(L_p\) spaces. Using an elementary method attributed to Favard, it proves a general criterion: when the normalized multiplier de…
This note extends inverse theorems from the constructive theory of periodic functions of one variable to functions of several variables. It establishes estimates for mixed finite differences of multivariable periodic functions in terms of best approximation by trigonometric polynomials of prescribed…
The paper develops a generalized solution theory for the mixed initial-boundary value problem for a general second order linear hyperbolic equation on a bounded star-shaped spatial domain, with right-hand side taken from a negative Sobolev-type Hilbert space. It defines suitable function spaces and …
This paper studies the general integral equation governing neutron slowing down in a spatial domain with absorbing boundaries, sources, boundary influx, absorption, and scattering by nuclei of varying mass. The neutron state is formulated in phase space using position, direction, and lethargy, and t…
This note studies the decomposition of tensor products of infinite-dimensional principal series representations of the proper Lorentz group, formulated through the locally isomorphic group of complex second-order matrices with determinant one. It first gives a unitary transformation showing that suc…
This paper formulates preliminary results on the analytic capacity of bounded plane sets, introduced in connection with the representation of continuous functions by uniformly convergent series of rational functions. It defines analytic capacity through bounded analytic functions on the complement o…
This paper studies the Cauchy problem for square systems of linear partial differential equations whose coefficients depend only on time, reducing the system to first order in time and analyzing it after Fourier transformation in the spatial variables. It gives conditions on the fundamental solution…
This paper studies linear extremal problems for weighted classes of analytic functions in finitely connected domains with rectifiable boundary, under minimal integrability assumptions on the weight. Using duality between boundary constrained classes and weighted approximation classes, it establishes…
The paper studies Favard and Zamansky’s problem of determining saturation classes for summation methods, focusing on the Hölder method of summation applied to Fourier series of continuous periodic functions. It derives the asymptotic behavior of the Hölder multipliers and proves that the Hölder meth…
The paper studies free multiplicative semigroups of real numbers whose counting function has a power density, and asks how the distribution of their generating elements follows from the distribution of all semigroup elements. Using elementary methods modeled on the arguments of Selberg, Shapiro, Ayo…
This paper proves an existence and uniqueness theorem for a multipoint boundary-value problem for a nonlinear system of ordinary differential equations. The argument compares the nonlinear problem with an auxiliary linear system, using a nonsingular change of variables, a matricant, and the associat…
This note strengthens earlier undecidability results in topology by shifting from homeomorphism of polyhedra to combinatorial questions about complexes. It defines a broad class of binary relations between complexes, lying between combinatorial equivalence and equivalence of fundamental groups for c…
This paper studies approximation and basis expansions for functions analytic in neighborhoods of an arbitrary continuum, extending classical results of Bernstein and Faber beyond level-line neighborhoods. It first proves a factorization and uniqueness result for conformal mappings of doubly connecte…
This note studies when weak local metric or angular conditions on a continuous complex mapping force analyticity. It defines preservation of angles, constant stretching, and an orientation condition at isolated image points, then proves several generalizations of results of Menshov and Bohr: angle p…
The paper addresses whether every normal topological space can be embedded in a bicompact extension preserving both weight and covering dimension. Using Smirnov’s theory of proximity and uniform spaces, it constructs suitable uniform structures from finite open coverings, with cofinal subfamilies co…
This paper studies boundary-value problems for a quasilinear second-order ordinary differential equation in which a small parameter multiplies the highest derivative. Under smoothness and stability assumptions on the coefficients, it develops asymptotic approximations by combining the degenerate fir…
This paper studies integral representations for functions of two complex variables in bounded complete bicircular domains. It characterizes the domains defined by parametrized boundary radii satisfying specified differential relations, showing that they coincide with bicircular domains with twice co…
The paper addresses uniqueness of generalized solutions to the Cauchy problem for conservative quasilinear hyperbolic systems, a question previously treated mainly for scalar equations or special systems. It proves a uniqueness theorem for piecewise-continuous and piecewise-smooth solutions of two-e…
The paper studies a boundary value problem with an oblique derivative for a generalized analytic function in a simply connected domain, reduced by conformal mapping to the unit disk and embedded in a one-parameter family. It transforms the problem into a system for three functions with a boundary co…
The paper studies the asymptotic behavior, as the accuracy tends to zero, of the epsilon entropy of compact classes of analytic functions bounded in a domain and measured on a continuum. For plane continua with elementary nondegenerate neighborhoods, it proves an exact quadratic logarithmic asymptot…
This note studies uniqueness of limit cycles for nonlinear oscillation equations of Lienard type and related planar systems. It establishes sufficient conditions, involving monotonicity properties of f(x)/g(x), transformed damping functions, and sign conditions at small and large amplitudes, under w…
The paper introduces a new space of nonempty closed subsets of a T1 space, denoted kappa X, with a topology designed to characterize continuous decompositions and mappings of compact Hausdorff spaces more effectively than the usual hyperspace. It establishes basic properties of this space, including…
This paper studies the maximal correlation coefficient for symmetrically distributed pairs of random variables, defining it through the first nontrivial eigenvalue of a normalized symmetric kernel associated with the joint density. It gives the corresponding variational characterization, describes a…
This paper develops a framework for homogeneous difference schemes for linear differential equations with variable coefficients, emphasizing convergence and accuracy uniformly over specified coefficient classes. It introduces definitions of convergence, approximation order, equivalence, symmetry, an…
This paper gives necessary and sufficient criteria for boundedness on the half-axis of solutions to linear differential equations with delayed argument, including variable delays and equations with both delayed and nondelayed terms. Working in Banach spaces, it formulates boundary-value problems wit…
This note studies lower bounds for the best uniform approximation of classes of differentiable and analytic functions by quotients of finite parameterized sums, including rational-type expressions. Using previously established entropy estimates, it derives inequalities for Hölder differentiable func…
