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 linear partially ordered topological spaces, defined as linear lattices equipped with a topology having a monotone neighborhood basis, thereby generalizing partially ordered Banach spaces without requiring bounds for infinite bounded sets. It establishes basic structural and con…
This paper studies singularly perturbed systems of ordinary differential equations in which the fast subsystem, for each value of the slow variable, has a unique rough stable limit cycle. The authors formulate an averaged equation for the slow variables by integrating the slow vector field over the …
This paper proves boundedness of a class of singular integral operators on Orlicz spaces over a bounded measurable domain. The kernel is assumed to satisfy cancellation, continuity, a Dini-type modulus condition in the angular variable, and Hölder continuity in the spatial variable, while the defini…
This note studies multidimensional convolution integral equations on a half-space and corresponding lattice difference equations, with data in standard Banach spaces of functions or sequences. For the continuous equation, the authors use a Wiener type factorization of the Fourier transform under a n…
The paper studies a Riemann type boundary value problem for two piecewise analytic functions on domains separated by a smooth closed contour, with boundary conditions involving derivatives and Fredholm integral terms. It introduces auxiliary integral representations for analytic functions under inde…
This paper studies approximation near the boundary of a domain whose boundary has analytic capacity zero. Using dual extremal formulations for analytic capacity and function-space duality, it proves criteria relating zero analytic capacity to approximation in boundary integrals by functions in Hardy…
The paper studies the indefinite form of the \(A\)-integral, defined through truncated Lebesgue integrals under a tail condition, and compares it with improper Lebesgue and Denjoy integration. It shows that existence of definite \(A\)-integrals on intervals does not generally yield well behaved inde…
This paper studies PS-isomorphisms, isomorphisms between the lattices or structures of subsemigroups, for torsion-free and ordered groups. It develops a sequence of lemmas on separable elements, isolated normal divisors, semi-Dedekind subsemigroups, and proper PS-isomorphisms, using these to show th…
This paper extends the method of steepest descent for solving nonlinear operator equations from finite-dimensional and Hilbert space settings to broader classes of Banach spaces. It formulates iterative schemes for potential and nonpotential operators, giving conditions on differentiability, monoton…
This paper studies when local stability, an external condition on a group of automorphisms, implies local nilpotency of the automorphism group itself. After formulating stability and local stability for automorphism groups, the authors prove that every finitely stable group of automorphisms of a fre…
This paper establishes existence results for nonlinear mixed initial boundary value problems for second order hyperbolic and parabolic equations in a strip, with nonlinear boundary conditions depending on boundary traces of derivatives and on a parameter. Under smoothness, Lipschitz, nondegeneracy, …
This paper develops the notion of conjugate manifolds on the Klein quadric representing lines of projective three-space and relates it to asymptotic manifolds defined by higher order contact with tangent hyperplanes. Using Cartan’s exterior forms and Grassmann products, the author applies this frame…
This note constructs an example of a web, equivalently a monotone continuous function of two variables, that cannot be approximated by rectifiable webs or by nomographable functions. It defines a metric deviation for webs, relates uniform convergence of functions to convergence of their correspondin…
This paper studies primitive integer points on the one-sheeted hyperboloid defined by b squared minus ac equals D, where D is an odd nonsquare positive integer, within a classical reduction domain. It proves an asymptotic distribution formula for points in suitable subdomains, expressed in terms of …
This note studies the problem of describing homomorphisms of commutative semigroups. It introduces decreasing ideal series and quasinilpotent semigroups, then proves that for a broad class of commutative semigroups with a principal decreasing ideal series, the structure can be decomposed into factor…
This note studies mixed boundary value problems for uniformly parabolic second order equations whose coefficients may have jump discontinuities across finitely many cylindrical interfaces. Using maximum principle arguments and auxiliary barrier functions following methods of Oleinik, the authors der…
The paper studies the Riemann problem, or decay of an arbitrary discontinuity, for a hyperbolic system of two first order quasilinear conservation laws. It defines a class of systems satisfying structural hyperbolicity and noncontact conditions, formulates stability conditions for admissible discont…
This paper studies uniqueness for the abstract Cauchy problem in a Banach space for a linear operator, distinguishing weak and strong solutions. It proves that if the spectrum is absent on a ray in the positive half-plane and the resolvent grows there with finite exponential degree, then the problem…
The paper introduces pseudonormal correlation as a mixture of two normal bivariate densities with opposite correlation coefficients, yielding normal marginal distributions but zero ordinary correlation, zero correlation ratio, and vanishing odd conditional moments. It then develops a broader family …
This paper examines local geometric conditions for equations of the form w = f(u,v) to be representable by a nomogram of aligned points. Starting from the determinant criterion for nomographability, it introduces associated functions that, after normalization, define coordinates of a point on the un…
This paper studies the error of multidimensional equal-weight quadrature formulas on the unit cube for function classes \(S_p\). Using Haar expansions and Hölder’s inequality, it derives an exact expression for the norm of the quadrature error in terms of a quantity \(\varphi_q\) determined by the d…
This paper studies when Banach spaces of bounded linear operators are themselves conjugate spaces. It first proves that a direct product, with the supremum norm, of conjugate Banach spaces is conjugate, then applies this result to show that the space of linear operators from a Banach space into a co…
This note studies the differential equation dx/dt = f(t,x) in a real Hilbert space, focusing on conditions for the existence, uniqueness, and qualitative behavior of bounded solutions. It first treats a linear equation with a bounded self-adjoint invertible operator, then extends the results to nonl…
This note gives explicit formulas for decomposing the tensor product of two supplementary series representations of the proper Lorentz group, complementing an earlier result on the irreducible components. The argument constructs an isometric realization of the tensor product space, applies the Planc…
This paper studies a fractional differentiation operator defined for Sobolev functions on a convex domain and compares it with fractional powers of elliptic partial differential operators. It establishes norm estimates for the operator in continuous and Lebesgue spaces under different Sobolev embedd…
This note studies orthogonal polynomials whose weight is supported on several disjoint intervals and vanishes on the intervening gaps, a case not covered directly by standard asymptotic treatments requiring nonvanishing weights except on small sets. Using rational functions on the associated two-she…
This paper studies lower bounds for the uniform distance between distributions of sums of independent identically distributed random variables and the class of infinitely divisible laws. Focusing on Bernoulli-type distributions with parameter \(p=n^{-2/3}\), it proves that the maximal distance for t…
This paper addresses Grothendieck’s question of whether every metrizable nuclear space can be isomorphically embedded in the space of infinitely differentiable functions on the real line. It proves a partial affirmative result: every complete metrizable nuclear space with a basis embeds in this func…
This paper examines whether transformation operators of Delsarte type, known for second order linear differential equations and generalized by L. A. Sakhnovich to higher order equations under analyticity assumptions, can exist for higher order differential equations with less restrictive coefficient…
This paper studies the spectrum of a non-self-adjoint second-order differential equation with continuous complex periodic coefficients, defining spectral points by the existence of a solution bounded on the whole real axis. Using the characteristic multiplier equation and the associated family of qu…
The paper studies central limit theorems for sums of the form \(\sum_{t=0}^{p-1} g(T^t x)\), where \(T\) is an ergodic endomorphism of a compact commutative group and \(g\) is a real \(L^2\) function. Using Fourier expansions in group characters, mixing properties of such endomorphisms, and semi-inv…
The paper studies a class of polynomials that are regularly monotone of a prescribed order on the interval [0,1], classified by alternating sign relations among successive derivatives and by specified type numbers. It constructs special normalized polynomials satisfying endpoint vanishing conditions…
This note studies Chebyshev sets in finite-dimensional Banach spaces, where each point has a unique nearest point in the set. Building on a theorem of Efimov and Stechkin for bounded sets, it argues that the boundedness assumption can be omitted by first showing that such sets are sets of existence …
This paper studies Borel summation methods for double series, focusing on sectorial summability methods denoted \(B_\lambda\) and \(B'_\lambda\), and their limiting forms \(B\) and \(B'\). It extends earlier regularity results by giving more general sufficient conditions under which a convergent dou…
This note studies biorthogonal systems generated by linear combinations of Mittag-Leffler type functions and analyzes their use in expansions on a finite interval. The authors establish an integral identity leading to biorthogonality, describe the zeros of the associated entire function including as…
This note studies the relationship between epsilon entropy, Kolmogorov widths, and nuclearity for centrally symmetric convex compact sets in Banach and locally convex spaces. It derives two-sided estimates connecting the epsilon entropy of a compactum with functions determined by its sequence of wid…
This paper extends several results on ordinary differential equations in Banach spaces to complete locally convex spaces for equations of the form dx/dt = f(x,t). It introduces an integral for functions with values in a locally convex space, records its basic properties, and uses it to reformulate d…
This paper introduces quasi-elliptic systems of differential equations with variable smooth coefficients, a class defined through weighted principal parts of the determinant and a nondegeneracy condition on the system. The class is shown to include elliptic systems in the Douglis and Nirenberg sense…
The paper applies solvability conditions of Chaplygin type to qualitative questions for operator and Volterra integral equations in partially ordered spaces. It formulates a comparison lemma for operators possessing a monotonicity property, then uses it for integral equations in Banach spaces equipp…
This paper studies the singular perturbation of a second order linear ordinary differential equation in a Banach space when a small positive parameter multiplies the highest derivative and tends to zero. Under smoothness and boundedness assumptions on the coefficients, with a positive scalar coeffic…
This paper studies implicit finite difference schemes for linear systems of partial differential equations with constant coefficients, focusing on reducing the computational complexity that arises in stable homogeneous two-layer schemes. It formulates the method of fractional steps, in which one tim…
This note gives sufficient conditions for complete continuity of embedding operators for Sobolev type spaces on unbounded Euclidean domains, including restrictions of functions to lower dimensional hyperplanes. It defines weighted spaces with fractional or integral smoothness and proves compactness …
The paper studies branching of solutions to nonlinear equations in Banach spaces when the derivative with respect to the unknown is a Fredholm-type operator with finite-dimensional kernel and cokernel. It gives a Lyapunov-Schmidt reduction for such equations, including cases relevant to nonlinear si…
This paper constructs examples of linear constant coefficient nonhyperbolic equations whose Cauchy problems nevertheless possess lacunas, addressing a gap left by earlier results on hyperbolic equations and finite domains of dependence. It studies a class of homogeneous operators whose characteristi…
The paper studies existence of solutions for nonlinear evolution equations in Hilbert space of the form v' + A(t,v)v = 0, using fractional powers of positive self-adjoint operators. It first establishes estimates and differentiability properties for the evolution operator associated with a time-depe…
This paper studies nontriviality criteria for certain Gelfand-Shilov type spaces of infinitely differentiable functions defined by growth bounds involving two sequences, and for related spaces of entire functions with prescribed exponential estimates. Using auxiliary entire functions and infinite pr…
This paper studies regularity and solvability for multidimensional elliptic variational problems and related quasilinear elliptic boundary value problems. It proves that a generalized minimizer with bounded first derivatives for a uniformly elliptic variational integral with Hölder smooth coefficien…
This paper studies scattering of plane waves for the wave equation with a nonstationary potential in three-dimensional space, using Fock radiation conditions to characterize outgoing waves. The scattering problem is reduced to an integral equation with the retarded Green function, and existence and …
The paper studies the construction of the Cauchy function for a linear ordinary differential operator of order n, a task equivalent to constructing a fundamental system of solutions and hence to integrating the corresponding Cauchy problem. It proposes an iterative approximation scheme beginning wit…
