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 paper studies boundedness of Calderón-Zygmund type singular integral transformations in weighted \(L_p\) spaces, extending results of Riesz, Babenko, and Stein. Using a method related to Hardy and Littlewood, it gives necessary and sufficient sharp ranges for several multidimensional weights, i…
This paper studies relationships among dyadicity, dimension, metrizability, and cardinal invariants for bicompact spaces, with particular attention to open images of products of metric compacta. It introduces openly dyadic bicompacta, establishes structural properties of this class, and proves metri…
This paper studies two person zero sum games whose payoff is a continuous function on the unit square, focusing on the size and structure of the set of games with unique optimal strategies. It proves that games with a unique solution and finite spectra of optimal strategies are dense in the space of…
This paper studies localization and convergence of Fourier series associated with fundamental systems of functions of the polyharmonic operator, a class that includes eigenfunction systems of nonnegative self-adjoint extensions of the minimal polyharmonic operator. Using earlier methods together wit…
A variational formulation is developed for the Helmholtz boundary value problem describing monochromatic wave propagation in a three dimensional waveguide with general smooth boundary and either impedance type or Dirichlet boundary conditions. The solution is expanded in prescribed transverse functi…
This paper introduces a boundary projection operator for finite multidimensional systems of linear difference equations with constant matrix coefficients, under a nonvanishing condition on the characteristic matrix on the unit torus. Using contour integral formulas for coefficient matrices, it const…
This paper studies groups of generalized motions in Riemannian spaces using the notion of defect of invariance for manifolds under continuous transformation groups. It defines the defect of a Riemannian space relative to a group, proves a coordinate invariant rank formula analogous to the Killing eq…
The paper studies two-layer, one-step iterative schemes for solving linear equations with positive non-self-adjoint operators in Hilbert spaces. It reduces implicit stationary iterations to explicit schemes and analyzes the norm of the transition operator in order to choose optimal or near-optimal i…
This note develops estimates for surface potential type singular integrals whose kernels depend on a generalized difference of arguments defined through a Bessel generalized shift operator. The authors introduce weighted fractional norms in a half space, relate them in the Hilbert case to norms defi…
The paper studies when the natural map from the inductive limit of the intersections of a subspace with the terms of a countable inductive system into the subspace has a bijective adjoint on duals. It relates this question to weak homomorphisms and surjectivity of adjoint operators, then uses invers…
The note develops new general integral representations for holomorphic functions in one and several complex variables, extending earlier operator methods introduced by the author. It defines composite inverse operator families and applies them to functions on star-shaped domains in one complex varia…
This note studies when optimality in a convex programming problem with concave, possibly nondifferentiable objective and constraint functions is equivalent to the existence of a saddle point of the corresponding Lagrange function. Using geometric separation arguments, limiting cones, and support fun…
The paper studies weak and generalized solutions of linear evolutionary systems whose spatial part is elliptic in the sense of Petrovsky, including cases beyond hypoelliptic equations and systems with complex-valued solutions constrained by cones. It develops several lateral smoothing estimates in l…
This paper studies the direct and inverse spectral theory for a half-line Sturm-Liouville equation whose potential has a singularity at the origin stronger than the Bessel type. Under specified growth, smoothness, and integrability assumptions on the singular part and perturbation, the authors estab…
The paper studies the multidimensional two-phase Stefan problem in a rectangular spatial domain, focusing on a regular classical solution with a moving phase-separation surface. For the two-dimensional case, with extension indicated to higher dimensions, the authors replace the Stefan condition by a…
The paper studies when compact Hausdorff spaces contain Stone-Cech compactifications of discrete spaces, reducing the problem to the existence of continuous maps onto Tikhonov cubes and to dyadic systems of zero-sets. It introduces the cardinal invariants massiveness and tightness, proves mapping th…
The paper studies boundary values and traces of generalized solutions of properly elliptic differential equations in a bounded smooth domain. Using Sobolev type spaces with boundary components and integration by parts identities, it proves equivalence between a norm involving interior Sobolev regula…
This note studies the location of points of maximal deviation in best uniform trigonometric approximation of continuous periodic functions. Extending related results for algebraic polynomial approximation, it analyzes differences of successive best approximating trigonometric polynomials, introduces…
The paper studies existence and uniqueness for nonlinear Hammerstein type integral equations and systems in Lebesgue spaces, allowing measurable sets of finite or infinite measure and avoiding assumptions such as complete continuity, self-adjointness, or restrictions like \(p \geq 2\). It formulates…
This paper studies Hamiltonian systems in action angle variables that are small perturbations of an integrable system, under a nondegeneracy condition on the Hessian of the unperturbed Hamiltonian near a fixed action value. A variational method is proposed, based on minimizing a functional that meas…
The paper studies the number of solutions to congruences modulo a prime power of the form F(x,y) congruent to 0 modulo p^m, where F is an absolutely irreducible polynomial and the variables range over incomplete residue intervals. Using a Hensel-type lifting argument, algebraic number theory, estima…
The paper studies weighted Sobolev-type spaces for functions on unbounded domains and addresses the failure of compact embeddings in such settings. For a broad class of unbounded domains, it establishes sharp weighted embedding estimates and compactness theorems for embeddings between spaces of diff…
The paper addresses P. S. Aleksandrov’s question on whether the small and large inductive dimensions must coincide for bicompact spaces. It constructs a Hausdorff bicompactum using lexicographically ordered compact continua, dense decompositions, marked transfinite sequences, Cantor set mappings, an…
The paper studies transitive subgroups of the finitary symmetric group on an infinite set, focusing on whether such groups can decompose as products of proper elementwise commuting normal subgroups. After establishing a lemma on the equivalence of the actions induced by an intransitive normal diviso…
This note studies optimization of cubature formulas for approximate integration of functions of many variables in weighted Hilbert spaces defined by Fourier transform weights. The full minimax problem is reduced to optimizing coefficients for fixed nodes, with special attention to lattice node syste…
This note relates the Schauder fixed point principle to stability questions for periodic solutions of nonlinear differential equations. It proves two abstract results for completely continuous operators in Banach spaces: a characterization of asymptotic stability in terms of isolation and index of a…
The paper studies a linear conjugation problem for a holomorphic vector with values in a Banach space of infinite sequences on a Lyapunov contour, with boundary relation determined by an infinite functional matrix. Under bounded invertibility and compactness assumptions on the matrix coefficient, it…
This paper studies minimax optimization problems of the form minimizing the maximum of a smooth function over an auxiliary set. It derives first-order stationarity conditions using directional derivatives of the max function and replaces generally discontinuous criteria by equivalent continuous func…
This paper studies averaging methods for nonlinear integro-differential equations with a small parameter, motivated in part by equations arising in the dynamics of imperfectly elastic bodies. It formulates and proves averaging theorems for systems with slow variables on finite intervals of order inv…
This note derives a central limit theorem for certain narrow-sense stationary random processes by reducing the problem to the known central limit theorem for stationary sequences of martingale differences. For an ergodic measure-preserving transformation and an associated decreasing filtration, it g…
The paper extends Berman’s study of functors on locally convex spaces by associating to each reflexive K-space with a suitable topologizing system a functor defined through spaces of measurable vector-valued functions. It proves comparison and representation results for these spaces, including condi…
This paper formulates and solves a finite control problem for a distributed linear system governed by a one-dimensional wave equation, seeking a boundary control that brings the system to rest in a prescribed finite time. The solution applies a Fourier transform in time, the Paley-Wiener theorem, an…
The paper studies almost sure growth rates for sums of independent random variables under moment conditions expressed through a general even increasing function g. It proves upper bounds of the form S_n = o(g^{-1}(A_n psi(A_n))) for functions psi whose associated series converges, with appropriate c…
The paper classifies Lie subgroups of the Lorentz group that have positive dimension and a finite group of connected components. Using the spinor representation of the Lorentz group and the known classification of its real Lie subalgebras, it determines the normalizers of the connected subgroups and…
The paper studies an extension of Zermelo-Fraenkel set theory obtained by adding a formal truth predicate for formulas under valuations, together with axioms governing this predicate. Within this system, the authors construct absolute natural transitive models of ZF and define ordinals that serve as…
The paper studies the existence, uniqueness, and construction of periodic solutions for differential equations in a complex Banach space with coefficients or nonlinear terms periodic in time. It develops fixed point operators related to Cesari’s method, first deriving criteria for first order linear…
This note studies intrinsic properties of strongly closed mappings between Hausdorff spaces, a class previously shown not to lower dimension. It establishes basic permanence results, including behavior under restrictions, inverse spectra with perfect projections, and directed systems, leading to the…
This paper examines representations of stationary electromagnetic fields in layered media as expansions in normal waves, formulated through differential operators associated with directions along and across the layers. It relates contour-integral methods based on residues to direct expansions in eig…
The paper studies derivability in a formal arithmetical calculus with equality, order, successor, and symbols for all primitive recursive functions, focusing on formulas provable without induction or with induction applied only after logical inferences. It defines a hierarchy of classes according to…
The paper studies nondeterministic numerical methods for the first Dirichlet problem for the Poisson equation in the unit square, with right-hand sides bounded in a Sobolev class. It constructs a randomized approximation based on values at order N squared points, using local orthonormal polynomial e…
The paper studies trace and extension problems for functions on Euclidean space whose Hilbert norms are defined by generalized Fourier type operators depending on a function of position and frequency. By reducing a smooth hypersurface to a coordinate hyperplane, it formulates conditions under which …
The paper studies finite-dimensional subspaces of Banach coordinate spaces for which fixedness, or asymptotic fixedness, of contractive linear operators on the subspace implies the corresponding property on the whole space. It formulates these questions in terms of saturated and completely saturated…
This paper studies limiting distribution functions for real multiplicative arithmetic functions through Zolotarev’s characteristic transform and summation theorems for multiplicative functions. It gives necessary and sufficient convergence criteria for the empirical distributions of values of a mult…
The paper gives a criterion for a T1 space to be homeomorphic to a metric space of covering dimension at most n: it must have a regular base whose element boundaries form a family of multiplicity at most n. Using properties of regular bases, locally finite refinements, and standard results from dime…
This paper studies global Cauchy problems for nonlinear first order equations, including multidimensional scalar conservation laws with bounded measurable initial data and a one dimensional Hamilton-Jacobi type equation with Lipschitz initial data. It introduces entropy-type definitions of generaliz…
The paper proves a duality theorem for the K-groups of homology and a slightly modified version of K-cohomology for subsets of a closed oriented homological manifold. For a decomposition of such a manifold into complementary sets A and B, under K-acyclicity assumptions in two adjacent dimensions and…
The paper proposes a method for treating extremal problems in the theory of univalent functions by applying Pontryagin’s maximum principle. Using the Löwner equation, it reduces the problem of minimizing the real part of a prescribed coefficient of \(G(f(z))\) over the class of normalized univalent …
This paper proposes a general iterative approach to minimizing nonlinear functionals on closed convex bounded subsets of reflexive Banach spaces, using convex Taylor-type approximations and an adaptive step-size rule. The main convergence theorem establishes monotonic decrease and, for convex functi…
This paper studies nonlinear multidimensional differential equations in finite-dimensional Banach spaces with almost periodic dependence on the independent variable. It derives algebraic conditions, based on a Frobenius-type complete integrability criterion and power-series representations, for comp…
