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
The paper studies conditions ensuring the existence of wave operators for pairs of self-adjoint operators, with emphasis on cases where trace class assumptions apply only to functions of the operators rather than to their difference. It proves that if the difference of the inverse operators is nucle…
This note addresses a question of S. L. Sobolev concerning the possible domains of membership of a function in fractional Sobolev, or Slobodetskii, spaces \(W_p^{(r)}(D)\), described in terms of the parameters \(\mu=r-n/p\) and \(r\). Using embedding and interpolation properties, such domains are kn…
The paper studies a Hilbert boundary value problem for an analytic function in a finite domain whose boundary condition couples values at a boundary point with values at its image under a Carleman shift. The authors reduce the problem to a singular integral equation and an associated system, establi…
The paper develops a non-iterative grid method for boundary-value problems for the Helmholtz equation in domains naturally described by polar coordinates, with emphasis on Dirichlet and Neumann problems in a disk. Using the method of lines in the angular variable, the periodic finite-difference coup…
This note studies Runge approximation in spaces of several complex variables, where the one variable Runge theorem does not generally extend. It proves a criterion: a domain is Runge precisely when its envelope of holomorphy is convex with respect to a class of holomorphic functions whose members ar…
The paper studies constant coefficient hypoelliptic equations in two variables whose real characteristic polynomial has real zeros with nonvanishing gradient. It constructs fundamental solutions by deforming integration contours around prescribed arcs of the real characteristic set, then derives the…
The paper develops a framework for additive set functions with values in Banach spaces, introducing norms, absolute continuity, translation continuity, generalized derivatives, and related spaces of Sobolev type. It establishes embedding and compactness criteria for these spaces and identifies sever…
This paper proves a representation theorem for continuous almost homogeneous additive functionals of a multidimensional Wiener process. It shows that, after localization on an increasing sequence of closed sets, such a functional can be written as the sum of a terminal difference of functions of the…
The paper addresses the construction of invariant differential forms and structural equations for infinite transformation groups defined by an involutive system of differential equations. Instead of following Cartan’s stepwise reduction to a Pfaffian system, it first constructs invariant forms for t…
This paper studies boundary-value problems for variational and partial differential equations in domains whose boundary has a degenerate contour, extending earlier Sobolev-type results to nonlinear, weighted, and intersection spaces. Using generalized Sobolev spaces and weighted spaces with boundary…
The paper studies two notions of final compactness in topology: compactness defined by the existence of countable subcovers, and compactness defined by complete accumulation points of uncountable sets. After proving several compactness lemmas for products of ordinal spaces, it constructs a completel…
This paper studies Gaussian, shift-invariant dynamical systems through the structure of the associated unitary ring of square-integrable functionals. Using generalized Hermite polynomial expansions, it identifies the shift automorphism of a one-dimensional normal dynamical system with a concrete aut…
This paper studies the unitary representation of the real matrix group of order n on the homogeneous space G/Gamma, where Gamma is the subgroup of integral matrices, using the method of horocycles. It classifies compact horocycles in this space by block upper triangular horocyclic subgroups associat…
This note studies Hausdorff bicompacta that are continuous images of ordered bicompacta, with particular attention to spaces satisfying the Suslin property. The authors introduce quasi-open and light mappings, show that such representations may be chosen for continuous images of ordered bicompacta, …
This paper determines the maximal dimension of complete groups of motions for Einstein spaces of nonconstant curvature when indefinite as well as positive definite metrics are allowed. Using the integrability conditions for infinitesimal motions in an orthonormal frame and a canonical analysis of th…
This note addresses Mal’tsev’s question concerning which degrees of unsolvability can occur for the word identity problem in finitely presented groups. Using reducibility by unrestricted Post tables, the argument combines a construction of Turing machines with prescribed enumerable-set degree, Boone…
This note studies empirical Bayesian estimation of a parameter when the prior distribution is unknown, but a long independent sample from the resulting mixture distribution is available, a setting called Robbins’ scheme. For a discrete random variable with distribution depending on a real parameter,…
This paper studies approximate solution of first-kind operator equations in Banach spaces when the inverse operator is not continuous. It proposes a scheme in which the unknown is restricted to a compact uniqueness class and approximated by an increasing sequence of finite-dimensional compact subset…
This note examines convergence of cubature and quadrature formulas from the viewpoint of order of proximity, contrasting it with convergence measured by the norm of the error functional on a Banach space. Sobolev reformulates the error functional as an operator acting on abstract functions with valu…
This paper studies extension problems for completely continuous operators with values in a Banach space and applications to fixed point theory. It proves that if such an operator is defined on a closed set, then it can be extended to the whole space so that its image lies in the closed convex hull o…
This paper studies invariant subspaces of real Volterra operators in a separable Hilbert space relative to a fixed involution. Using characteristic operator functions, it establishes a criterion for \(S\)-unicellularity: a Volterra \(S\)-real operator is \(S\)-unicellular precisely when the set of i…
This note studies analytic solutions of the Tricomi equation near the origin and in the entire complex plane, using a representation of solutions in terms of two analytic functions of one variable. Boundary value problems are considered in which values are prescribed on the line y = 0 and on curves …
The paper studies small smooth perturbations of hyperbolic automorphisms of the torus, focusing first on the two-dimensional case. Using successive approximations, it constructs invariant expanding and contracting families of nonclosed curves for the perturbed map, then proves a simultaneous straigh…
This note solves the third order linear ordinary differential equation with variable coefficients x squared y triple prime plus 3 x y double prime plus y prime plus x squared y equals 0 by an operational method. After a change of variables, the equation is related to an operator of the form d/dt, t …
This paper studies extremal values of the chromatic number among connected simple graphs with a fixed number of vertices and edges. The authors define upper and lower chromatic numbers for the class of connected graphs with n vertices and p edges, then prove exact formulas for both quantities. The p…
The paper studies minimal systems, total conjugate systems, and quasi-complements in separable Banach spaces. It proves that a complete minimal system in a subspace, under a totality condition on its conjugate system, can be extended to a complete minimal system in the whole space with a total conju…
This paper studies when a topological space can be recovered from the semigroup of its continuous self-transformations. It proves that completely regular spaces containing a simple arc are characterized up to homeomorphism by isomorphism of these semigroups, using the minimal two-sided ideal of cons…
This paper studies the classification up to isomorphism of formal Abelian groups over an algebraically closed field of characteristic \(p > 0\), within the class for which multiplication by \(p\) is an isogeny and whose unipotent component consists only of additive groups. Using Dieudonné module met…
This paper constructs a canonical symmetric affine connection on a Hermitian manifold, using the fundamental skew tensor associated with the metric and almost complex structure. Starting from Lemlein’s pencil of symmetric almost symplectic connections, it imposes additional invariant conditions invo…
This paper studies Cauchy-type integrals and boundary-value problems for generalized analytic functions satisfying a first-order conjugate equation on closed Riemann surfaces of genus greater than two. It constructs modified Cauchy kernels without eigenfunctions, derives integral representations, an…
The paper studies spaces of Banach-valued additive set functions introduced by Sobolev and relates their direct and inverse embedding properties to operator theory. It proves norm identities showing that such set functions generate continuous, absolutely continuous, or completely continuous linear o…
This note characterizes total boundedness of a metric space in terms of the remainder of its bicompact extension associated with the metric proximity. It proves that a metric space is totally bounded if and only if this remainder is hereditarily normal, using a reduction to a countable uniformly dis…
This paper generalizes Ambartsumian’s inverse Sturm-Liouville uniqueness theorem from an interval to bounded two- and three-dimensional domains with Neumann boundary conditions. It proves that, for a bounded potential in the perturbed Laplace eigenvalue problem, convergence of the series of eigenval…
This note proves a Wiener-type theorem for functions represented by absolutely convergent Walsh series on the unit interval. The argument treats these functions as a complete normed ring, after passing to a compact zero-dimensional space in which dyadic rational discontinuities are separated, and sh…
This paper studies infinitesimal bendings of a simply connected convex surface of positive Gaussian curvature under a generalized sliding boundary condition, in which the displacement vector is required to be perpendicular along the boundary to a prescribed non-tangent vector field. The argument red…
This note establishes an a priori estimate for solutions of a parabolic equation with zero boundary or initial data, under boundedness, continuity, and modulus conditions on the coefficients and forcing term. Using a probabilistic representation and trajectory continuity estimates for the associated…
The note studies Hall-type properties of finite groups relative to a set of primes, focusing on existence, conjugacy, containment, and solvability of corresponding Hall subgroups. It introduces the notion of a Pi-suitable subgroup and proves a generalization of a theorem of Philip Hall: if a normal …
This paper develops criteria for complete continuity of linear and nonlinear integral operators between Lebesgue spaces on finite measure domains, with particular attention to unbounded kernels. Using compactness in measure, equiabsolute continuity of integrals, and truncation of kernels, it proves …
This note studies groups in which cyclic subgroups of prime order, restricted to a fixed set of primes, are complemented, called primitively pi-factorizable groups. It introduces pi-primitive groups and elements and proves structural characterizations for periodic such groups, including descriptions…
This note proposes a construction and classification of irreducible representations of Dickson Chevalley simple algebraic groups over a finite field, using representations induced from one dimensional characters of a maximal nilpotent subgroup. It establishes two central results: every irreducible r…
This note studies the large time asymptotic behavior of a one dimensional free boundary problem for the heat equation on a moving interval with prescribed values at both endpoints and prescribed spatial derivative at the free boundary. Assuming the boundary data and flux converge to constants, with …
This paper studies analytic functions in essentially bounded tube domains and relates their geometry to Fourier transforms and normed convolution rings on convex cones. It proves that maximal ideal spaces of weighted convolution rings are closures of tube domains of holomorphy of prescribed type, an…
Efimov studies complete simply connected two-dimensional Riemannian manifolds of everywhere negative Gaussian curvature and asks when they can be regularly isometrically immersed in three-dimensional Euclidean space. The paper relates this problem to the growth of the reciprocal square root of the a…
This note studies trace, or boundary value, questions for differentiable functions of several variables whose selected partial derivatives have finite Lp norms, especially in anisotropic classes and in domains more general than coordinate half-spaces. It proves estimates for lower derivatives and es…
This note generalizes Faith’s decomposition theorem for associative rings by treating an arbitrary supernilpotent Kurosh radical rather than only the Jacobson radical. It proves that if the factor ring by such a radical satisfies the minimum condition for principal right ideals, then the ring decomp…
The paper studies principal boundary value and mixed problems for one dimensional parabolic equations whose coefficients have first kind discontinuities along finitely many moving lines. Using heat potential methods, fundamental solutions constructed by Pogorzelski, and estimates due to Gevrey, the …
The paper studies the first boundary value problem for general elliptic differential equations of order 2m in bounded domains whose boundaries may have angular, conical, or otherwise nonsmooth points. It develops weighted integral inequalities near boundary points satisfying exterior accessibility o…
This paper studies the completeness of the positive fragment of Heyting’s intuitionistic propositional calculus under Kolmogorov’s interpretation of formulas as problems. It defines finite problems by finite sets of admissible possibilities and solution subsets, introduces conjunction, implication, …
The paper studies fixed singular points of generalized analytic functions satisfying a first order generalized Cauchy-Riemann equation with coefficients regularized by analytic functions that may have poles or essential singularities. It formulates the problem of constructing solutions with a prescr…
The paper develops an asymptotic method for linear differential equations in Hilbert, and under stated assumptions Banach, spaces whose operator coefficients contain slowly varying terms and rapidly oscillating factors depending on a small parameter. The solution operator is decomposed according to …
