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 factorization of complex matrix polynomials satisfying the symmetry condition A(lambda) equals A*(-conjugate lambda), motivated by applications in stability, optimal control, and differential games. It gives necessary and sufficient conditions for representing such a polynomial as …
This paper gives criteria for estimating the rotation, or topological degree, of finite-dimensional vector fields that do not vanish on the boundary of a bounded domain. It proves nonnegativity results for fields in even-dimensional real spaces whose derivatives commute with matrices having no real …
This paper classifies Harish-Chandra modules for the group SL(2,C), understood as representations whose dense subspace decomposes algebraically with finite multiplicities under a maximal compact subgroup. It constructs elementary modules from associated homogeneous functions, describes their composi…
This paper studies a Cauchy problem for second order hyperbolic equations containing a small positive parameter, with initial data that produce an initial jump in the singular limit. It constructs a matched asymptotic expansion in powers of the parameter, combining regular terms satisfying reduced f…
The paper studies traces of functions in anisotropic Sobolev spaces on smooth hypersurfaces under a condition relating the minimum and maximum smoothness indices. Building on a general characterization of trace spaces by an integral equation with kernel determined by the surface and the Sobolev norm…
The paper studies the decomposition of the tensor product of two irreducible maximally degenerate unitary representations of the group of complex matrices of order n with determinant 1, for n at least 3. Using a modification of the horosphere transform method of Gelfand and Graev, the tensor product…
This paper studies harmonic vector functions in the upper half-space satisfying generalized Cauchy-Riemann conditions, with emphasis on multidimensional analogues of classical results on conjugate harmonic functions. It defines Hardy-type classes H^p and S^p, gives a Fourier-transform characterizati…
The paper studies local questions in Banach analytic spaces where closed subspaces need not be complemented, a difficulty that obstructs direct extension of finite-dimensional analytic arguments. It introduces a completeness condition and proves existence and factorization results for finite-dimensi…
The paper introduces the polyhedron defined by positive quadratic forms with fixed arithmetic minimum and develops its basic properties in the coefficient space of quadratic forms. It shows that this polyhedron is locally finite, invariant under integral unimodular transformations, has vertices corr…
This paper studies infinitely divisible probability laws whose alpha-components are all infinitely divisible, a subclass arising in the theory of decompositions of probability laws. It gives a sufficient condition, distinct from earlier criteria of Linnik, for a law with a compound Poisson type Lévy…
The paper proves a decomposition theorem in dimension theory: an n-dimensional cube cannot be represented as a countable union of proper closed subsets whose pairwise intersections have dimension at most n minus 2. The argument extends Urysohn’s two-set result by using continua joining opposite face…
This paper studies illumination from within of the boundary of unbounded convex bodies in Euclidean space, where a boundary point is illuminated by another if the open segment between them lies in the interior. It proves that the entire boundary of an unbounded convex body is internally illuminable …
This note studies the existence of Poisson-stable solutions for differential equations in Banach spaces, allowing nonunique solutions and without assuming global solvability for all initial data. It develops a method of limiting transformations based on convergence of shifted functions, compactness …
This note studies the boundary behavior of regular solutions to uniformly elliptic second order equations in bounded domains whose boundary points admit inner or outer contact by generalized paraboloids. Using barrier constructions and assuming the maximum principle, it establishes lower estimates n…
This note formulates the approximate solution of nonlinear operator equations in Banach spaces as a controlled process in which different iterative methods are switched according to an admissible control. It introduces optimization problems that seek either the best accuracy under a cost bound or th…
This paper examines relations among topological entropy, Kolmogorov epsilon entropy, and metric entropy for homeomorphisms of compact metric spaces. It proves that topological entropy can be obtained as the limiting growth rate of the epsilon entropy of orbit metrics, and establishes, for compact me…
The paper studies equivalence relations among absolute bases in Köthe spaces, focusing on when bases are equivalent up to isomorphism, scalar multiplication, and permutation. It introduces the multiplicity of a basis as the minimal number of regular subsequences needed after permutation, defines Ris…
The paper develops a generalized form of Lyapunov’s second method for systems with small perturbations, including stability with respect to only part of the variables in the neutral case. It replaces standard definiteness requirements on a Lyapunov function and its derivative by conditions involving…
The paper studies complete orthonormal systems of Laplace eigenfunctions in bounded domains and the corresponding spectra of nonnegative self-adjoint extensions of the minimal Laplacian. It first shows that in one dimension, for an interval or a finite union of intervals, the fundamental numbers hav…
This note studies exact upper bounds for best approximation of differentiable periodic function classes by trigonometric polynomials in the uniform and integral metrics. For classes whose r-th derivative has a prescribed convex modulus of continuity, the author proves that the extremal error is atta…
The paper studies topological spaces defined by generalized distance functions, especially continuous, weakly continuous, and semicontinuous o-metrics, symmetric o-metrics, and Delta-metrics. It formulates analytic conditions on these functions and proves several metrization and structural results, …
This paper studies fundamental systems of functions for the Beltrami operator on a Riemannian domain, a framework that includes trigonometric systems and eigenfunctions of elliptic boundary value problems without imposing boundary conditions. It proves a mean value formula for regular solutions of t…
This paper studies probabilistic properties of pairwise Hamming distances among a random subset of vertices of the n-dimensional unit cube, where vertices are chosen with independent Bernoulli coordinates. For prescribed distance intervals, it analyzes the counts of pairs whose distances fall in eac…
This paper studies the existence of values in differential pursuit games in Euclidean space, where two players choose measurable controls under standard continuity, Lipschitz, compactness, and growth assumptions. It defines piecewise-programmed strategies and examines three payoff types: terminal di…
This paper studies the large-time asymptotic behavior of solutions to the exterior Neumann boundary-value problem for the two-dimensional wave equation outside a convex contour with positive bounded curvature. The solution is decomposed into a free Cauchy-wave part and a correction term, whose Lapla…
The paper studies two singular integral operators on rectifiable Jordan curves and associated nonlinear integral equations in subspaces of Lp characterized by modulus of continuity conditions. It derives norm and continuity estimates, including analogues of Zygmund type inequalities, under generaliz…
This paper constructs a compactification of a noncompact symmetric Riemannian space using admissible projective representations of its motion group. Starting from the root system and lattice of the space, it defines a family of boundary, or epsilon, spaces associated with admissible tuples in Cartan…
The paper develops a regularizer for pseudodifferential Cauchy problems with complex symbols and for multilayer difference schemes, using bicharacteristics and a canonical operator on a Lagrangian manifold with a complex germ. It proves existence, uniqueness, and propagation of smoothness for a clas…
This paper studies homogeneous generalized functions on the space of rectangular matrices over a non-discrete locally compact disconnected field, focusing on the analytic family defined by powers of the maximal norm of the maximal minors. It determines the poles and residues of these generalized fun…
This paper studies separable topological groups containing a Weil-complete almost metrizable normal subgroup, in the sense that the subgroup contains a compact set of countable character. It proves that for such a group G with normal subgroup H, one can choose a subset A of G meeting every coset mod…
The paper studies a boundary value problem posed by A. V. Bitsadze for the three-dimensional Lavrentiev-Bitsadze equation, which is elliptic in one half-space, hyperbolic in the other, and degenerates on the separating plane. For a bounded domain bounded partly by characteristic cones, it introduces…
This note states and outlines a proof of a rigidity theorem for compact manifolds of constant negative curvature: if two such manifolds of dimension at least three have isomorphic fundamental groups as abstract groups, then they are isometric. The argument equips the common finitely generated group …
This note studies covering problems for plane analytic sets in Baire space whose vertical sections satisfy a hereditary property. Using Lyapunov’s general theorems on multiple separability, it gives a construction that covers an analytic set, or the relevant sections of such a set, by a Borel or coa…
The paper studies the analytic structure of Hilbert subspaces generated by homogeneous random fields on Euclidean space, reducing the problem through the spectral representation to weighted spaces generated by exponentials over bounded parameter sets. For rectangular sets, it gives sufficient logari…
This note proposes a real analogue of Pyatetskii-Shapiro’s construction of Siegel domains, defined from a vector space with involution, a homogeneous convex cone, and a definite Hermitian bilinear mapping. It proves that homogeneous Siegel domains are affinely homogeneous, then specializes the const…
This paper studies the stability of relaxation processes for minimizing a differentiable functional on a convex domain in a real Hilbert space under strong monotonicity and Lipschitz type bounds on its derivative. It analyzes perturbed iterations with additive noise, measuring perturbations first by…
This note studies sequential estimation for scalar parametric families, comparing non-Bayesian sequential plans with fixed-sample Pitman estimation under constraints on expected sample size. Under smoothness assumptions expressed as absence of discontinuities in information quantities, the authors s…
This paper reports a computational verification of Fermat’s Last Theorem for all odd prime exponents below 5500 using Vandiver’s criterion for irregular primes, together with Kummer’s result for regular primes. Computations on the BESM-6 computer rechecked earlier SWAC results below 4002, extended t…
This note studies a form of modeling finite pseudo-Boolean algebras by systems of arithmetical formulas under Kleene realizability, in connection with realizability of propositional formulas and intuitionistic arithmetic. It defines when such a system models an algebra, proves by induction that alge…
The paper studies error estimation for finite difference solutions of the Dirichlet problem for the Laplace and Poisson equations in a bounded plane domain. It derives weighted a priori estimates for the grid solution and for difference approximations to derivatives of arbitrary order, with dependen…
The paper constructs several compact Hausdorff spaces for which the covering dimension and the small and large inductive dimensions do not coincide. Using modified topologies obtained by replacing points of the square with circles or previously constructed compacta, it gives examples with dim equal …
This note studies boundary behavior of the Poisson integral in a half-space and applies it to the Dirichlet problem for the Laplace equation with very general boundary data. It states several Fatou-type results showing when derivatives and mixed derivatives of the Poisson integral converge to corres…
The paper studies conditions under which topological and metrizable spaces can be compactified or condensed onto compacta, with special attention to points of noncompactness and non-pi-compactness. It shows by examples that compactifiability onto compacta is not determined simply by the correspondin…
The paper studies uniqueness for the Cauchy problem for general linear partial differential equations with constant coefficients and zero initial data, under growth restrictions imposed only on one spatial half-axis rather than on the whole line. Using the Newton-Puiseux asymptotics of the roots of …
The paper studies Darboux problems for a second order hyperbolic equation whose coefficient of the second \(x\)-derivative may vanish on the boundary line, allowing parabolic degeneration. Using a weighted energy identity, an exponential change of unknown, and suitable choices of weights, it proves …
The paper proves that the Hilbert parallelepiped, or Hilbert cube, cannot be represented as a countable union of proper closed subsets whose pairwise intersections are weakly infinite-dimensional. The argument develops several auxiliary results on weakly infinite-dimensional spaces, normal adjoining…
This paper studies a differential game of approach in which two players choose constrained controls entering jointly, rather than separately, in the system dynamics. It formulates the problem in the class of mixed approximating strategies, introduces extremal strategies and a modified notion of posi…
This paper examines borderline conditions for convergence in the L metric of trigonometric Fourier series and their conjugate series. It constructs a summable periodic function whose integral modulus of continuity, and that of its conjugate function, are both of order 1 divided by log 1 over delta, …
This note studies the optimization of algorithms for numerical differentiation, numerical integration, and interpolation on classes of functions modeled by generalized Sobolev-type Hilbert spaces. Using the functional-analytic principle of minimizing the norm of the corresponding error functional, t…
This note revisits a theorem of M. V. Keldysh and M. A. Lavrentiev concerning boundary behavior of nonconstant harmonic functions attaining their lower limiting value at a boundary point, with implications for uniqueness in the Neumann problem. It extends the result from a three-dimensional parabolo…
