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 the growth of Lebesgue functions associated with uniformly bounded orthonormal systems on the interval and its consequences for Fourier series. It proves that such systems necessarily have Lebesgue functions with at least logarithmic growth on a set of positive measure, in the sens…
The paper extends Bernstein’s averaged interpolation processes from real intervals to the complex domain for functions regular in a bounded domain with analytic Jordan boundary and continuous on its closure. Using interpolation nodes obtained from a conformal mapping of the exterior of the domain an…
This paper studies oscillatory and capture phenomena in a class of second order differential equations with periodic time dependence, including the Sitnikov-type restricted three-body problem with two equal masses and a massless third body. Under stated regularity, monotonicity, and integrability as…
The paper studies the spectrum of quantum mechanical energy operators for molecular systems under prescribed permutation, rotational, and reflection symmetries, with pair potentials satisfying stated regularity and decay conditions. Using decompositions of the particle system into subsystems and the…
This note studies sufficient conditions for the Szegő limit formula for Toeplitz determinants associated with a nonnegative integrable function on the unit circle. Using parameters defined from the moments, the associated outer function, and orthonormal polynomials on the circle, it proves that for …
This paper studies problem E for a class of nonlinear elliptic equations that degenerate parabolically on part of the boundary, of the form \(y^m u_{yy}+u_{xx}-f(x,y,u,u_x,u_y)=0\) in a simply connected domain in the upper half-plane. Under differentiability, monotonicity, and boundedness assumption…
This paper addresses the existence of closed convex surfaces whose principal radii of curvature satisfy a prescribed relation \(f(R_1,R_2)=\varphi(n)\), extending classical cases associated with Christoffel and Minkowski. Using the support function formulation, elliptic equations on the sphere, uniq…
This paper studies convergence rates for coordinate relaxation methods applied to a positive definite quadratic functional in finite dimensional Euclidean space, allowing general control sequences in which each coordinate recurs arbitrarily far along the iteration. Using an error measure defined by …
This note studies a generalized M. Riesz identity for trigonometric polynomials and uses it to investigate when a convolution operator defined on polynomials of order at most n admits a norm-preserving extension to periodic function spaces. It establishes general criteria and examples for such exten…
This paper studies Markov processes on a countable state space specified by transition density coefficients and asks how such processes can be continued after the first accumulation time of jumps. Under a finiteness condition expressed through nonnegative bounded solutions of the eigenvalue equation…
This note studies boundary zero-sets of simply connected plane domains in the compactification by prime ends under homeomorphisms whose coordinate functions have finite Dirichlet integral. It introduces a metric condition for a boundary set, expressed by divergence of an integral involving the Hausd…
This note studies the extension of functors from the category of Banach spaces to the category of separable locally convex spaces of type alpha. Using the representation of alpha spaces by spectra of Banach subspaces, local completion, beta strengthening, and limits in the category of alpha spaces, …
This paper develops interpolation theorems for linear and quasilinear operators on symmetric Banach function and sequence spaces, expressed through conditions on their fundamental functions or sequences. These results are applied to operators generated by Fourier coefficients, yielding estimates for…
This paper studies finite-dimensional representations of bicompact topological semigroups, focusing on when such representations, especially irreducible ones, separate points. It proves that every totally disconnected bicompact topological semigroup has enough representations by finite semigroups, a…
The paper studies the asymptotic behavior of solutions to the Dirichlet problem for the Laplace equation near an irregular boundary point, using spherical sections of the domain and eigenvalues of the Beltrami operator to control radial growth. It proves comparison estimates for boundary norms, uniq…
The paper addresses the problem of constructing an invariant equipment for an m-dimensional surface in a space with affine connection, allowing arbitrary ambient dimension and possible curvature and torsion. It develops a tensorial method based on higher order tangent spaces, covectors annihilating …
This bibliographic notice surveys recently published books and collected volumes in mathematics and mathematical physics, with emphasis on differential equations, boundary-value problems, functional analysis, operator theory, numerical methods, and related computational programs. It provides publica…
This paper studies weighted function spaces on the positive orthant whose smoothness is governed by dominant mixed derivatives, motivated by boundary questions for degenerate hyperelliptic equations. It defines weighted analogues of Sobolev, Besov, and Nikol’skii type spaces using mixed derivatives,…
This paper studies transcendence and algebraic independence of values at nonzero algebraic points of certain hypergeometric E-functions and their derivatives. It strengthens a coefficient arithmetic lemma used in Shidlovskii’s method by allowing different prime ideals for different subintervals of t…
This note studies the real Euclidean analogue of reconstructing a function in three-dimensional affine space from its integrals over straight lines belonging to a three-parameter complex. The authors formulate the space of lines as a pseudo-Riemannian manifold, identify the relevant Laplace-Beltrami…
This note studies two notions of local cohomology at a point in a paracompact Hausdorff space: the direct limit of the reduced cohomology of punctured neighborhoods and the inverse limit of relative cohomology groups. Using an exact sequence obtained from the Leray spectral sequence for the inclusio…
This paper introduces elliptic boundary and coboundary morphisms for Sobolev sections over a closed smooth manifold with an embedded submanifold, combining pseudodifferential operators with restriction and adjoint restriction maps in a matrix framework. It formulates ellipticity through the usual sy…
Two-dimensional autonomous systems of the form \begin{equation} \dot{x}=P(x,y),\quad\dot{y}=Q(x,y)\tag{1} \label{1} \end{equation} are considered, where the right-hand sides have isolated singular points $O_j$ of the pole type. The concept of a "quasi-residue" $J_j$ of a singular point $O_j$ is intr…
This paper develops a theory of differentiation for mappings between real linear topological spaces, not necessarily normed, using derivatives defined by uniform convergence on specified systems of subsets and with respect to chosen subspaces. It introduces first and higher derivatives, including we…
This note studies boundary regularity of spatial quasiconformal mappings in three-dimensional Euclidean space. Extending known interior Hölder estimates, it uses modulus estimates for separating surface families, including an inversion lemma, to prove Hölder continuity at boundary points for mapping…
This paper develops finite difference schemes for boundary value problems for degenerate elliptic equations and for related degenerate parabolic equations in bounded domains where coefficients may vanish on part of the boundary. The authors specify how boundary or boundedness conditions depend on th…
This paper proves several metrization results for feathered, or p, spaces under normality and covering assumptions. It first shows that a weakly paracompact p-space with a G-delta diagonal has a uniform base, yielding metrizability in the paracompact case, and then establishes that a collectionwise …
The paper generalizes the classical Radon transform from Euclidean hyperplanes to spaces of real and complex rectangular matrices and to real and complex Grassmann manifolds. It defines integration over matrix planes given by first-degree matrix equations, establishes basic invariance, homogeneity, …
A topological classification of the singular points of the system $$dx^i=\sum_{\mu=1}^{n-1}\sum_{j=1}^na^i_{j\mu}x^j\,dt^{\mu}\quad(i=1,\dots,n),$$ is provided, assuming that the conditions of complete integrability are satisfied, and the $n\times n$-matrices $(a^i_{j\mu})$, $\mu=1,\dots,n-1$ have n…
This paper studies permutations of the parameters labeling irreducible representations of the Lie groups G2 and SU3 that leave representation characters, equivalently Casimir operator eigenvalues, invariant. Explicit transformation sets are given for the two groups and interpreted geometrically as r…
The paper studies the exceptional case of paired integral equations of convolution type in weighted Banach spaces, where the operator symbol is allowed to have zeros of finite integer order on the real axis. It introduces the notion of a left equivalent normalizer and constructs such an operator to …
It is proved that in linear boundary value problems, the property of a parameter being an eigenvalue or a regular value is preserved under small changes in the delay. Bibliography: 6 items.
The paper studies approximation of periodic functions by linear summation methods for Fourier series, using moduli of smoothness, best trigonometric approximation, conjugate functions, and bounded subadditive operators. It establishes direct and inverse estimates for iterated convolution differences…
This paper studies plane and axisymmetric filtration problems with free boundaries in inhomogeneous media, focusing on cases where the image of the filtration domain in the complex potential plane is known. The problems are formulated as inverse mixed boundary value problems for a system generalizin…
The Galerkin method is used to solve the mixed problem $$\begin{aligned} \frac{\partial^2u}{\partial t^2}&=\frac{\partial}{\partial x}\biggl(p(x)\frac{\partial u}{\partial x}\biggr)+f(t,x,u,u_t,u_x), \\ u(0,x)&=\varphi_0(x),\quad u_t(0,x)=\varphi_1(x), \\ u(t,0)&=u(t,\pi)=0, \end{aligned} \tag{1}$$ …
The paper considers a spectral problem for a system of first-order ordinary linear differential equations of the form \begin{gather} \frac{dY}{dx}=AY+f\tag{1}, \label{1} \\ \alpha Y(a,\lambda)+\beta Y(b,\lambda)=0\tag{2}, \label{2} \end{gather} where \begin{equation} A=A(x,\lambda)=\lambda A(x)+\sum…
This note studies the normal solvability of a generalized Abel integral equation and its adjoint, including a compact perturbation term, by reducing them to conjugate singular integral equations with a Cauchy kernel. It establishes identities connecting fractional Abel-type operators with Cauchy sin…
The paper studies fundamental solutions for linear singular partial differential operators of B-elliptic type involving the Bessel operator in a half-space. Using weighted plane-wave expansions and F. John’s method, it derives integral representations for fundamental solutions in the constant-coeffi…
Sufficient conditions are established for the dissipativity of systems \begin{gather}\dot{x}=y,\quad\dot{y}=-yf(x,y,t)-g(x)+e(t),\tag{1}\\\dot{x}=y-f(x,y,t),\quad\dot{y}=-g(x)\tag{2}\end{gather} in the case where the function $f$ satisfies substantially different constraints for $x>x_0>0$ and for $x…
The paper addresses the localization problem for Fourier series with respect to arbitrary fundamental systems of functions of the Laplace operator in an arbitrary multidimensional domain, including eigenfunction expansions for standard boundary value problems and multiple trigonometric Fourier serie…
