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 the Cauchy problem for the Laplace equation with analytic data by analytically continuing the equation, the data, and the Cauchy surface into a complex domain. For three and four variables, it constructs local integral representations of the holomorphic solution using the character…
The paper develops a duality theory for locally convex topological vector groups over the real or complex field endowed with the discrete scalar topology. It establishes Hahn-Banach type separation results, weak closure properties, and a characterization of compatible locally convex vector space top…
This note develops refinements of a Tauberian theorem of M. V. Keldysh concerning the recovery of asymptotic information on increasing functions from integral transforms. Under assumptions on the behavior of Stieltjes or ordinary integral transforms in a complex region bounded by a curve, the author…
This note studies approximately optimal properties of Wald tests for testing statistical hypotheses in parametric families under regularity conditions on the likelihood and its derivatives. It estimates the accuracy of Wald’s asymptotic optimality results by proving normal approximation and concentr…
The paper studies polynomial approximation in the mean on the boundary for analytic functions in Smirnov classes \(E_p\), \(p>1\), on simply connected domains whose rectifiable Jordan boundary belongs to a class defined by boundedness of the Cauchy singular integral in \(L_p\). Using a generalized m…
This paper studies the sharpness of known upper estimates for the convergence of derivatives of Lagrange and Hermite interpolation polynomials on Chebyshev type nodes for functions whose first derivative has a prescribed modulus of continuity. It constructs, for each degree, special functions in the…
This paper studies how regularity properties behave under products of the form Phi(f(x))f'(x), in contrast with the often worse behavior of the superposition Phi(f(x)). It proves that if Phi is absolutely continuous and f is differentiable with absolutely continuous derivative, then Phi(f(x))f'(x) i…
This note establishes necessary and sufficient conditions for a boundary point to be regular for the Dirichlet problem for a uniformly parabolic second-order equation with bounded Hölder coefficients in an arbitrary domain. Using Wiener’s method of generalized solutions and a parabolic potential ass…
This note studies differential games in which one player seeks to drive the state of a nonlinear controlled system to a closed terminal set in minimum time while the other seeks to prevent it. To avoid difficulties caused by discontinuous positional strategies, the paper introduces sigma strategies,…
This paper extends earlier results on finite projection spectra of topological spaces to infinite spectra formed from directed families of decompositions and partitions, using nerves of coverings and their limit spaces. It introduces completeness relative to a family of decompositions, analyzes spac…
The paper studies homogeneous locally symmetric domains in generalized conformal spaces of signature \((p,q)\), reducing their classification to the algebraic problem of determining suitable defining planes in the Lie algebra of the conformal transformation group. It proves that every such plane is …
This paper studies metric criteria for functional series whose coefficients range over Banach spaces of numerical sequences, emphasizing situations where classical results such as Landau’s theorem do not apply because convergence is only almost everywhere or in measure. It gives necessary and suffic…
The paper studies singularly perturbed systems of ordinary differential equations in which a small parameter multiplies the derivatives of the fast variables, focusing on cases where the associated fast system has a degenerate equilibrium or a degenerate limit cycle. Under specified nondegeneracy an…
The paper formulates estimates for double sums over arbitrary complex sequences weighted by quadratic characters, represented by Jacobi or Kronecker symbols. Its main theorem gives a decomposition into a possible main term from square arguments and an error bounded by the minimum of several expressi…
The paper studies the high energy distribution of eigenvalues for self-adjoint ordinary differential operators on the whole line generated by even order formally symmetric expressions with polynomially controlled coefficients. Under growth, regularity, and phase space integrability assumptions, it p…
The paper studies an extended category of locally trivial principal G-fiberings, in the sense of Gelfand and Fuks, after restricting bases to spaces satisfying the second axiom of countability. It constructs the corresponding universal fibering from nondegenerate n-frames in a countable product of l…
This paper studies the far-field behavior of stationary solutions to the three-dimensional Navier-Stokes flow-past problem for an exterior domain, focusing on the axisymmetric case with finite Dirichlet integral. It proves that every such axisymmetric solution satisfies Finn’s decay condition, by de…
The paper studies cooperative games whose core may be empty and seeks conditions under which a von Neumann, Morgenstern stable set nevertheless exists. It introduces auxiliary games on two parts of a partition of the player set, defines conjugate characteristic-function bounds for the two subgames, …
The paper studies high-frequency asymptotics for subsequences of eigenvalues of Dirichlet and Neumann boundary-value problems for the Helmholtz equation in a multidimensional bounded domain, focusing on eigenfunctions localized near stable one-dimensional extremal cycles. Using the ray method, the a…
This paper studies Hölder continuity of generalized solutions in \(W_2^1(D)\) for a class of strictly elliptic divergence form equations whose lower order coefficients and free terms belong to mixed norm spaces. Since these spaces may include functions outside the integrability range covered by stan…
This paper studies nonassociative algebras over a fixed commutative associative ring with identity that contain no nilpotent elements, in the sense that x squared equals zero only for x equal to zero. It gives necessary and sufficient conditions, involving a conditional associativity type identity a…
This paper studies homogeneous subsets of absolutes and the possibility of obtaining new extremally disconnected topological groups from orbits of ultrafilters under groups of homeomorphisms. It proves that such orbits are homogeneous extremally disconnected subspaces of the absolute, gives decompos…
This note introduces integral transforms associated with the first order differential operator in time that appears in a mixed boundary value problem for a second order elliptic operator with parameter. Motivated by the need to treat general time dependent boundary data in the contour integral metho…
This note develops a topological analogue of Słupecki’s theorem for continuous mappings on selected compact spaces. Using an Ostrand form of the Kolmogorov, Arnold superposition theorem, it proves a representation theorem for continuous maps from powers of a connected finite polyhedron into the circ…
This paper studies criteria for faithful matrix representations of solvable torsion-free groups over fields of characteristic zero, in relation to Mal’tsev’s theorem on solvable matrix groups. It introduces conditions using powered locally nilpotent groups, finite rank, and compatible inner automorp…
This paper studies the Hilbert-type singular integral with summable density on a finite interval and estimates how its local \(L_p\) size and modulus of continuity depend on corresponding characteristics of the density. For \(1<p\leq\infty\), the authors prove integral inequalities relating \(\Omega…
The paper develops an iterative method for solving a class of integral equations in potential theory when the usual Neumann series is obstructed by a nearest eigenvalue. A general theorem is proved for completely continuous operators in a Hilbert space, showing convergence of an iteration on the ort…
The paper studies efficient trajectories in a positively homogeneous dynamic model of production, formulated through superlinear set-valued mappings between ordered cones and encompassing discrete variable-technology models and continuous convex programming problems. It establishes compactness and e…
The paper proposes a generalization of linear elliptic boundary value problems in which prescribed boundary data on part of the boundary are supplemented by an equality condition linking values on another boundary portion to values on an interior diffeomorphic image. The authors examine the model ca…
The paper studies duality relations between beta and delta characteristics of Banach spaces, defined through extremal averages over families of subspaces. It introduces a convex function transformation related to the Legendre transform, establishes its inversion properties, and applies it to connect…
The paper studies boundary value problems for a class of second order systems of composite type whose characteristic polynomial has one multiple family of real characteristics, focusing on a canonical system previously derived by the author. It formulates a boundary value problem with mixed conditio…
The paper studies continuous mappings under which covering dimension is constrained more sharply than in classical Hurewicz-type inequalities. It introduces the notion of a strongly closed mapping and proves that if such a mapping sends a normal space onto a paracompact space, with image dimension a…
This paper studies decompositions of a linear operator on a vector space over an arbitrary field, relative to the direct sum of generalized eigenspaces associated with a chosen subset of the field. It proves that, for any scalar outside this subset, an operator can be written as a sum of two operato…
The paper constructs an algebraic framework for studying Hadwiger’s conjecture by assigning to each finite simple graph a polynomial in countably many variables, defined recursively through edge deletion and contraction and initialized on disjoint unions of complete graphs. It defines analogues of t…
This paper studies stabilization as time tends to infinity for solutions of the heat equation in the generalized Cauchy problem with initial data in the distribution space \(S'_{1/2}(R^n)\). It defines a generalized spherical limiting mean for the initial functional and shows that, when this mean ex…
This paper studies sequential estimation plans for basic Markov processes, focusing on first-entry stopping rules and the extent to which such plans are determined by properties of their stopping times. For binomial and multinomial schemes, Poisson processes, and Brownian motion with unknown drift, …
The paper studies the relationship between the Teichmüller metric on the space of marked compact Riemann surfaces of genus p and invariant metrics on the Siegel upper half-plane induced by the period matrix map. It proves that the maximal normalized invariant Finsler metric on the Siegel space gives…
This paper studies power stability of finite difference approximations for time-dependent mixed problems with constant coefficients, using the spectral framework of Godunov and Ryabenkii for families of evolution operators. It introduces generalized eigenvalues of the characteristic equation and ana…
The paper studies the Dirichlet problem for uniformly elliptic second order equations in divergence form whose lower order coefficients may be discontinuous and unbounded, but belong to mixed norm spaces rather than ordinary Lebesgue classes. It develops embedding and interpolation estimates for mix…
This paper studies generalized Gaussian stationary processes whose spectra have asymptotic power-law behavior, focusing on analytic descriptions of the associated Hilbert spaces with reproducing kernels. Using canonical representations for multiplicity-one processes and Wiener-Hopf type equations, i…
This paper studies pseudodifferential operators on smooth compact Riemannian manifolds with boundary, acting on Bessel potential spaces of sections of Hermitian vector bundles. It defines boundary indicators as families of Wiener-Hopf operators, formulates fitted boundary problems and related equipm…
This note defines a class of strictly hyperbolic difference operators intended to preserve key properties of strictly hyperbolic differential operators on sequences of grids. Using Fourier representations on the grid, it formulates homogeneity, regularity, and root separation conditions analogous to…
The paper develops an algorithm for constructing higher order approximations in the averaging method for systems of ordinary differential equations with a small parameter and a periodic right hand side. By successive changes of variables, each remainder is shown to satisfy an equation of the same st…
The paper studies uniform structures of borderings on completely regular spaces, a concept related to Smirnov’s characterization of compact extensions with controlled remainder dimension. It defines such structures by axioms analogous to uniform structures of open covers, proves that the subfamily o…
This note studies Sobolev type problems for pseudodifferential equations when boundary conditions are imposed on a submanifold that is not the boundary of the ambient manifold and has multidimensional singularities. The argument localizes the problem near the singular submanifold, applies a Fourier …
This note studies stability of closed, possibly discontinuous, Phi-minus operators between locally convex spaces under compact and precompact perturbations. It establishes sufficient conditions under which a perturbation of a Phi-minus operator remains Phi-minus, extending earlier results for Fréche…
This paper studies crossed products of type II1 factors by finite groups of outer automorphisms, with emphasis on preservation of approximate finiteness for hyperfinite factors. It proves that if a separably acting type II1 factor is approximately finite, then its crossed product by a finite outer a…
This paper studies positive, or bounded below, solutions of evolutionary hypoelliptic equations, stated primarily for uniformly Petrovskii parabolic equations of arbitrary order with real variable coefficients. Using auxiliary functions, Green’s formulas, interior and boundary estimates, and invaria…
