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 derives asymptotic estimates for the error norms of cubature formulas in weighted Sobolev type spaces \(H_2^{(\mu)}(\Omega)\), under regularity and growth assumptions on the weight function. It introduces cubature formulas with a boundary layer regular in the sense of S. L. Sobolev, charac…
This note studies density and trace properties in weighted Sobolev spaces, with weights depending on the distance to a boundary or to a coordinate hyperplane. It gives conditions under which functions in first order weighted spaces on a cube can be approximated in the weighted norm by smooth functio…
This note studies elementary representations of a connected semisimple complex Lie group, obtained by analytic continuation of the principal series and parametrized by characters of a Cartan subgroup. It defines spectral bases and indicators for these signatures and proves a criterion for complete i…
This paper develops a general relaxation method for finding a point common to a family of closed convex sets in a linear topological space, using generalized projections defined by a nonnegative distance-like function. Under stated compactness, convexity, and continuity conditions, it proves converg…
The paper studies remainder terms in multidimensional central limit and asymptotic expansion theorems for normalized sums of independent identically distributed random vectors with finite moments. It addresses whether logarithmic factors in known convergence estimates for convex or Borel sets can be…
This note proves an analogue of the Radó-Cartan removability theorem for solutions of second-order elliptic equations. For a continuously differentiable function satisfying a linear elliptic equation off the boundary of its zero set, under standard Hölder regularity assumptions on the coefficients, …
The paper studies when a primitive-recursively closed class of functions admits a finite basis from which all functions in the class can be obtained by substitution alone. It proves that such a class has a finite basis exactly when it contains a universal function for its unary members, deriving con…
This paper studies the defect of the abstract Cauchy problem \(dx(t)/dt=Ax(t)\) for a closed linear operator in a Banach space, especially when the operator domain is not dense. It defines the defect as the dimension of the quotient between the closure of the domain and the closure of the initial ma…
This paper develops a projection method for studying bounded lower semicontinuous solutions of elliptic inequalities in a domain of Euclidean space. It defines lower and upper projections of a function onto planes and shows that, under assumptions involving absolute continuity of the support mapping…
The paper introduces the class of predicates defined as the intersection of s-rudimentary predicates with predicates computable by a Turing machine with logarithmic slowdown, and compares it with several previously studied restricted classes used in Kleene normal form and enumeration theory. It prov…
The paper studies simple bases, minimal complete systems that cannot be simplified by identifying variables, for closed classes of functions in the algebra of logic. Building on Post’s classification of closed Boolean function classes and known criteria for completeness via precomplete subclasses, i…
The paper studies subgroups of free polynilpotent groups, defined through iterated terms of the lower central series and viewed as free groups in products of nilpotent varieties. Extending earlier results on free soluble groups, it gives a criterion for when a subgroup lying between successive itera…
This note derives identities in the general theory of orthogonal polynomials for sums involving derivatives, complementing the Christoffel-Darboux formula for orthonormal polynomial systems on an interval. It proves formulas for the kernel sum of first derivatives, its diagonal specialization, and c…
This paper develops multidimensional analogues of results on decompositions of probability laws, especially Raikov’s theorems on holomorphic characteristic functions and infinitely divisible laws without Gaussian components. It proves that a characteristic function holomorphic in a ridge domain cont…
This paper studies the Cauchy problem for the evolution equation dx/dt equals Ax in a Banach space, where A is a closed densely defined unbounded operator, and relates well-posedness to resolvent estimates and semigroup properties. It introduces the well-posedness set and the uniform well-posedness …
The paper treats nonstationary diffusion in plane multilayer media whose diffusion and linear interaction coefficients vary discontinuously from layer to layer. It generalizes an operational method previously used for heat conduction without sources by applying layerwise exponential substitutions an…
This note studies the partially ordered set of attracting sets, defined as omega-limit sets of points, for a continuous self-map of an interval. It formulates structural properties of this order, including the existence of minimal and maximal elements in maximal chains, classifications of maximal el…
This note proves a multidimensional analogue of a classical convergence theorem for holomorphic functions, formulated for sequences of harmonic functions in three variables. It shows that if selected first partial derivatives of a harmonic sequence converge to zero under specified uniform and pointw…
This paper studies a nonlinear programming problem in which the objective is the sum of a linear function and a fractional linear term under convex constraints, with emphasis on the case of linear equality constraints and nonnegativity. It establishes basic properties of the fractional linear object…
This note studies the representation of continuous linear functionals on spaces of holomorphic functions in convex domains of complex Euclidean space. For a convex domain containing the origin, it introduces a conjugate set defined by nonintersection with complex hyperplanes and uses an integral rep…
This note addresses the decision problem for fragments of the narrow predicate calculus, comparing satisfiability and finite satisfiability for classes defined by quantifier prefixes and predicate vocabularies. It proves that formulas without equality with prefix pattern forall exists forall followe…
This paper studies direct and inverse scattering for multidimensional partial difference equations defined by a bounded self-adjoint finite-difference operator with a finite real perturbation. Using resolvent kernels and a limiting absorption principle, it establishes existence and uniqueness of sol…
This paper studies generalized differentiation and quasilinear differential operators for functions whose first generalized derivatives are locally finite measures, with particular attention to discontinuous functions. It introduces upper and lower representatives defined through directional average…
This paper studies the inverse spectral problem for a half-line Dirac system with locally integrable real coefficients. It first shows that the spectral function does not determine a general system uniquely, because orthogonal transformations preserve the spectral measure, and therefore reduces the …
This paper studies an inverse scattering problem for a non-self-adjoint Sturm-Liouville operator on the half-line with complex potential satisfying an exponential integrability condition and Dirichlet boundary condition at the origin. It introduces suitable notions of denominator, scattering functio…
This paper describes representations of commutative symmetric separable Banach algebras with identity in a separable Pontryagin space of finite negative index. It first recalls the Hilbert space case as a direct integral over the space of symmetric maximal ideals, then analyzes the indefinite case b…
The paper studies the Cauchy problem for second order hyperbolic equations whose type may degenerate on the initial line, with particular attention to conditions ensuring well posedness when lower order terms are present. It formulates refined integral criteria for existence, uniqueness, and stabili…
This paper studies integral representations for functions of exponential type expressed in polar coordinates in two complex variables, including functions regular in a half-space and entire functions. It introduces a harmonic function defined by an integral transform and shows, through analytic cont…
This note studies multiplier methods for summing Fourier series, focusing on estimates for the mean absolute value of the associated kernel under convexity or concavity assumptions on the multiplier array. It proves an upper bound in terms of the final multiplier, derives a simple sufficient conditi…
The paper applies Chaplygin’s method to a nonlinear boundary value problem arising in the equilibrium of a membrane without contour chain forces. It constructs explicit lower and upper functions that bound the solution, establishes uniqueness in the considered smoothness class, and develops a monoto…
This paper studies solvability of nonlinear operator equations of the form BF(x) = x in a Hilbert space, where B is a linear self-adjoint operator that may be unbounded and indefinite. Extending earlier variational results that required boundedness and strong restrictions on the positive spectrum, i…
The paper develops a framework for defining second order elliptic differential operators in functional derivatives on infinite dimensional spaces, including cases where the coefficient operator is unbounded. Using Hilbert space scales and trace class criteria, it defines operators of the form involv…
This paper studies equilibrium measures and equilibrium potentials for closed subsets of an n-dimensional parallelepiped with respect to a broad class of decreasing singular kernels satisfying an integrability condition and an additional growth monotonicity condition. Using capacity, variational arg…
The paper studies global regular realization in three-dimensional Euclidean space of infinite strips in complete two-dimensional metrics of negative curvature, with the metric written in semigeodesic form and satisfying bounded \(C^{4,1}\) regularity and curvature bounds between negative constants. …
The paper studies refinements of Sobolev type embedding theorems by replacing target Lebesgue spaces with rearrangement invariant Lorentz type spaces defined through decreasing rearrangements. It establishes embedding relations for the spaces \(L(\lambda_1,\lambda_2,p)\), proves a strengthened poten…
The paper studies Cauchy problems for general linear systems of partial differential equations in Gevrey spaces, focusing on sufficient and necessary regularity weights for solutions analytic in one variable. Using the quasi-characteristic polynomial and Puiseux expansions of its roots, it gives a s…
The paper addresses whether the classical nilpotency of the Frattini subgroup of a finite group extends to finitely generated linear groups, and more generally to linear groups over finitely generated subrings of a field. It develops a refinement of Mal’tsev’s finite approximation method by showing …
The paper studies an analytic problem motivated by statistical tests and unbiased estimation, concerning module homomorphisms defined by multiplication by a matrix of holomorphic functions on a bounded polycylinder. For the ring of holomorphic functions satisfying polynomial-type growth estimates ne…
This note studies uniqueness for the second and third boundary-value problems for a second-order uniformly elliptic equation with nonpositive zeroth-order coefficient, in bounded domains whose boundary may contain singular points where no boundary condition or regularity is prescribed. It introduces…
This paper extends Pogorzelski’s theorem on the invariance of a weighted Hölder-type class of functions under Cauchy-type singular integrals. For a finite system of arcs with possible corner or nodal endpoints, it proves that an integral with a shifted singularity preserves the class under specified…
This paper studies extremal problems for univalent conformal mappings of annuli and more general multiply connected domains under prescribed separation and containment conditions on boundary components and marked points. It establishes sharp lower bounds for distances between images of boundary circ…
The paper addresses the construction of cubature formulas with regular boundary layers for rational convex polyhedra in arbitrary dimension, where geometric intuition is replaced by lattice and face combinatorics. It develops a framework in which boundary layer coefficients are grouped by sublattice…
