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 introduces a family of function spaces defined through the variation of local polynomial approximation errors on cubes. It develops distribution estimates, embedding results, and a decomposition theorem showing that functions in these spaces can, outside sets of small measure, be represent…
This paper studies observability for a class of nonlinear differential equations in a Hilbert space with a Lipschitz nonlinear term and a possibly noninvertible observation operator. It introduces exact, finite time approximate, and asymptotic approximate observability, then constructs an auxiliary …
This note extends Carleman’s quasianalyticity criterion to linear operators in Banach spaces, asking when bounds on iterates of an operator imply that the vector is zero. For operators without spectrum, the argument relates quasianalyticity of the sequence of bounds to the growth of the entire resol…
The paper studies boundary behavior of multidimensional quasiconformal and related monotone Sobolev mappings using the notion of Bessel capacity of type (1,n). It proves that for a monotone mapping of a ball belonging to the class W_n^1, angular boundary values exist at all boundary points except fo…
This note studies a boundary value problem with a large complex parameter for a second order elliptic system in a three-dimensional domain, motivated by contour integral methods for parabolic mixed problems with time derivatives in the boundary condition. Under spectral, smoothness, and boundedness …
This note extends parts of the theory of strongly continuous operator semigroups to semigroups that are strongly continuous only for positive time and may have a singularity at zero, provided the singularity is summable after multiplication by a power of time. It defines classes of semigroups \(L^{(…
The paper characterizes relatively projective closed ideals in Banach algebras of continuous functions on a compact space. It proves that a closed ideal in C(Omega) is projective as a C(Omega)-module precisely when its spectrum, the corresponding open subset of Omega, is paracompact. The sufficiency…
This paper studies a global computational approach to regularization for evolution problems governed by positive definite self-adjoint differential operators, contrasting it with local time-stepping methods. The authors discretize the full space-time problem at once, reduce it to a system of linear …
This note constructs two compact Hausdorff spaces illustrating a separation between covering dimension and inductive dimensions. The first example, using Suslin’s hypothesis and the continuum hypothesis, is a completely normal bicompactum obtained from a product of a Suslin continuum with an interva…
The paper develops a continual integral representation for the fundamental solution of a broad class of parabolic type differential equations, motivated by limitations of earlier measure based generalizations of Wiener and Feynman formulas. For equations with polynomial symbol \(P(x,\xi)\) of even o…
The paper establishes duality statements for coherent analytic sheaves on a complex analytic manifold countable at infinity. It equips Čech cohomology and Dolbeault cohomology with natural locally convex topologies, identifies them canonically, and then relates continuous duals of spaces of global D…
The paper develops a method for solving differential equations whose variable coefficients include delta functions and their derivatives, motivated by models combining continuous structures with discrete concentrated elements. It first formulates a class of partially degenerate operator equations, t…
This note studies uniform convergence criteria for Fourier series of Bohr almost periodic functions whose Fourier exponents have a single limit point, considering separately the cases where the exponents tend to infinity or to zero. The criteria are formulated through rates of decrease of best appro…
This paper studies the asymptotic behavior of generalized Bayes posterior densities and posterior mean estimates for independent samples from parametric families, allowing the prior factor to be a measurable function rather than necessarily a probability density. It identifies normalizing factors an…
This paper studies elliptic boundary value problems for systems of linear differential equations in a smooth bounded domain when the boundary condition degenerates on a smooth codimension one submanifold of the boundary. The authors introduce weighted Sobolev-type spaces adapted to the degeneracy an…
This note studies the rate of uniform approximation of continuous periodic functions by partial sums of their Fourier series, using best trigonometric approximation and quantities measuring the tails of Fourier coefficients or remainders in related \(L_q\) metrics. It proves an estimate for \(\|f-S_…
The paper introduces condition R for varieties of universal algebras, a strengthening of the embedding theorem for partial algebras, and studies its consequences for free extensions, free closures, and free products. Under this condition, it proves analogues of the Nielsen-Schreier, Kurosh, and Grus…
The paper studies stability of abstract three-level operator difference schemes in a Hilbert space, extending earlier stability results expressed in compound norms to estimates in standard energy norms associated with the scheme operators. Under positivity, Lipschitz continuity in time, and the cond…
This note addresses a problem posed by Maskit concerning the existence of fundamental domains for finitely generated Kleinian groups. It reviews the relevant notions of regular and limit sets, forms the quotient of the regular set by the group, and analyzes its components as Riemann surfaces covered…
The paper studies a generalized class of convolution type integral equations on the real line with bounded measurable coefficients having generalized limits at infinity, in a range of Banach function spaces including Lebesgue, bounded measurable, and continuous function spaces. By decomposing the op…
This paper studies the topological classification of normally solvable boundary value problems for Petrovskii elliptic systems in a simply connected planar domain. Using the invariant subspace associated with the upper half-plane spectrum of the principal symbol, the authors express normal solvabili…
This paper develops a duality framework for convex multidimensional variational problems involving partial derivatives. It first defines Banach spaces generated by normal convex integrands, closely related to Orlicz spaces, and describes their duals, including absolutely continuous and singular comp…
This paper addresses Efremovich’s problem of characterizing which boundary homeomorphisms of the absolute spheres of two \(n\)-dimensional Lobachevsky spaces are induced by equimorphisms of the spaces. It proves that, for \(n \geq 2\), such an equimorphism exists if and only if the given boundary ma…
This paper studies function spaces generated by measurable modular functions, called genfunctions, on sigma-finite measure spaces, extending earlier Musielak and Orlicz constructions under weaker hypotheses. It gives necessary and sufficient conditions for the associated space to admit a normal F-no…
The paper studies completeness of systems of analytic functions of the form F(z, a_n), where F is generated by a power series with coefficients forming a complete analytic system and {a_n} is a sequence of complex numbers. Using a criterion that reduces completeness to uniform approximation of the g…
The paper introduces theta-uniform spaces as a generalization of uniform spaces compatible with a topology, using theta-coverings of locally finite type by canonically open sets. It shows that every theta-uniformity induces a theta-proximity and that theta-uniformities on a space correspond to ordin…
This paper studies stability of two-level operator difference schemes on Hilbert spaces with respect to right-hand side perturbations, extending earlier stability results for initial data. Using energy norm estimates and the method of separating stationary inhomogeneities, it derives bounds for solu…
The paper studies time-optimal control problems in Banach spaces with phase constraints, where admissible controls generate trajectories that must satisfy set-valued and functional restrictions. Using separation-type functionals defined on reachable and target sets, it establishes criteria for contr…
This paper introduces a weight function for finite incidence structures with block multiplicities and uses it to study structures whose block sizes belong to a prescribed finite set and whose weights on all subsets of fixed size are specified. By double counting incidences within each equiblock comp…
The paper extends triangular representation and characteristic function factorization results for bounded operators close to unitary operators, allowing invertible operators whose spectra need not lie on the unit circle. For operators T on a separable Hilbert space with I minus T*T in a symmetricall…
This paper studies weighted approximation of functions on the real line by algebraic polynomials with the Gaussian weight exp(-x²/2), using weighted Lp norms. It proves an inverse-type estimate for an antiderivative F of a function f, showing that the best weighted polynomial approximation error of …
This note studies spectral synthesis for invariant subspaces of the shift operator in weighted sequence spaces and the corresponding classes of analytic functions in the unit disk. It relates synthesis to quasianalyticity and uniqueness theorems for functions smooth up to the boundary, formulating c…
The paper studies spectral expansions and Riesz means associated with arbitrary nonnegative self-adjoint extensions of the Laplace operator in arbitrary domains, including cases with point, continuous, or mixed spectrum. Combining earlier methods for spectral expansions with Gårding’s theorem, it es…
This paper studies the local sample path structure of separable Gaussian fields on compact spaces with continuous covariance kernels. Using the Mercer, Hilbert-Schmidt expansion of the covariance operator, it establishes almost sure pointwise representation of the field by its spectral series, then …
This note extends generalized Cauchy, Schwarz, and Poisson integral formulas associated with systems of weight functions in the class considered by Dzhrbashyan and in the author’s earlier work. It introduces two systems of functions and the corresponding moment sequences, then defines transformed Ca…
The paper studies the first boundary value problem for a second order elliptic equation in a planar domain where the equation degenerates parabolically on part of the boundary. Using Sobolev space formulations, adjoint integral identities, and a priori estimates under sign and boundary coefficient c…
This paper studies convergence of products of non-identical probability measures on compact groups, asking whether representatives can be chosen from each right-translate class so that every sequence of such representatives has a convergent product. It defines complete sets of measures, proves closu…
This paper develops a nonlinear analogue of the Newtonian, or Riesz, potential adapted to the study of \((p,l)\)-capacity in Euclidean space for \(p>1\), \(pl<n\). Using Fourier-defined Sobolev-type spaces and an associated energy for generalized functions and measures, it establishes potential-theo…
The paper studies generalized differentiation of continuous functions of two variables and related summability properties of double trigonometric Fourier series. It defines several mixed, symmetric, averaged, and circular difference quotients and proves existence theorems showing that a continuous f…
This note studies linear, integral, convolution, and superposition operators in generalized Hölder spaces defined by a concave modulus function. It proves continuity of positive linear operators between such spaces, establishes automatic continuity for integral operators under mapping assumptions, a…
This paper studies when a subspace of a countable inductive limit of locally convex spaces is itself determined by the induced inductive system, either at the level of duals or topologically. It introduces conditions M0 and M for inductive limits and proves necessary and sufficient criteria for prop…
This note generalizes Craig’s theorem on the independence of quadratic forms in independent standard normal variables. It considers a quadratic polynomial Q and an arbitrary polynomial statistic P of a multivariate normal vector, and proves that P and Q are independent if and only if an orthogonal c…
This paper studies the non-self-adjoint differential operator \(Ly=-y''+p(x)y\) in \(L^2(-\infty,\infty)\), where \(p\) is complex-valued, with emphasis on square-integrable solutions and discreteness of the spectrum. Using an analogue of Prüfer’s substitution, the second-order equation is reduced t…
This note studies Euler normal classes for smooth immersions and embeddings, focusing on immersions homotopic to a fixed immersion and on embeddings of closed nonorientable manifolds in Euclidean space. In the metastable range it describes the realizable normal classes of immersions in terms of the …
This paper studies cardinal invariants of Hausdorff bicompact spaces, especially the Suslin number, bitightness, and the character and height of points. It introduces the notions of height, bitightness, and divergence, establishes closure and decomposition lemmas for compact spaces, and uses them to…
This paper studies vibrostability for differential equations in which a state depends on a time-varying control and, in particular, on the derivative of that control, a setting motivated by systems with hysteresis such as elastic-plastic elements. It defines vibrostability as the continuous extendab…
This note formulates an optimal stabilization problem as a two-person differential game for controlled systems with an integral performance functional and opposing control components. For the linear time-varying case, it gives a necessary and sufficient condition for the existence of an optimal admi…
This paper studies idempotents in crossed products of groups and associative rings, focusing on the subgroup generated by the group elements occurring in the finite support of an idempotent. It proves that the support subgroup of any central idempotent in an arbitrary crossed product is a finite nor…
