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 Hilbert linear conjugation problem for holomorphic vectors on a Lyapunov surface, with Hölder continuous boundary data and a matrix coefficient satisfying a positivity condition expressed through its minors. By reducing the boundary value problem to a system of singular integra…
This paper develops an approximate solution method for rectangular boundary value problems for the biharmonic equation with homogeneous conditions on the function and its normal derivative. A 13 point finite difference analogue is formulated, and the associated eigenfunctions and eigenvalues of the …
This paper derives asymptotic formulas and bounds for trigonometric sums of the form \(\sum_{x \leq P}\exp(2\pi i ax^n/p^t)\), where \(P=(p^t)^{1/r}\) and the parameters lie in specified ranges. Using a reduction to shorter sums, a previously established estimate for polynomial exponential sums, and…
This paper studies Fredholm integral equations of the first kind, formulated as Ax equals f in a Hilbert space with A a completely continuous linear operator. It derives necessary and sufficient solvability conditions in terms of orthogonality to solutions of the adjoint homogeneous equation and a c…
This paper solves an extremal problem for q-quasiconformal mappings of the unit disk onto plane domains containing two prescribed points, normalized by fixing 0 and a, where a differentiable real function of finitely many image points is to be maximized. Using variational methods for conformal and q…
The paper proves local existence for a one-phase Stefan-type free-boundary problem for a heat equation with piecewise constant coefficients and transmission conditions at an internal interface. Using auxiliary moving boundaries, maximum-principle comparisons, and an approximation by delayed free-bou…
The paper studies diffusion type equations with first and second functional derivatives on a Hilbert space scale, using a negative norm completion to accommodate generalized random processes. It defines Gaussian measures on this space and derives integral representations and uniqueness results for C…
The paper proves an existence and uniqueness theorem for generalized polynomials formed from a Chebyshev system of continuous functions on an interval, with prescribed interpolation values that are to occur as an alternating sequence of local extrema at suitably chosen nodes. The argument strengthen…
This paper studies a quadratic variational problem in Hilbert space associated with a bounded linear operator and proves existence and uniqueness of the minimizer, characterized by a linear operator equation. The general result is specialized to pairs consisting of a distributed term and an initial …
This note studies vector-valued countably additive mappings from a ring of sets into a complete separable real locally convex space, comparing several natural classes defined by bounded variation, continuity, boundedness, extendability to the closure of the ring, and countable additivity. Using vari…
The paper studies a property of solutions to the elliptic Monge-Ampère equation \(u_{xx}u_{yy}-u_{xy}^{2}=1\) in a finite simply connected convex domain with prescribed boundary values. For the convex solution with positive second derivatives, it introduces a change of variables based on the first d…
The paper studies the Cauchy problem for a class of linear differential operator equations whose left hand side is a product of powers of factors of the form T minus lambda X, where T is an ordinary differential operator in time and X is an operator in the spatial variables. Under stated smoothness …
This paper develops harmonic analysis on the one-sheeted hyperboloid viewed as a homogeneous space of the connected group preserving a quadratic form of signature \((1,n-1)\), with noncompact stabilizer. Using spherical functions associated with invariant generalized functionals, it describes the co…
This note introduces systems with quotients as a lattice-theoretic framework extending the Lesieur and Croisot theory of sigma algebras, allowing a unified additive theory for ideals in nonassociative rings and groupoids, submodules over nonassociative rings, and normal subgroups under commutator mu…
This paper studies the locally convex space of holomorphic functions on an open subset of the complex plane with arbitrary isolated singularities, constructed as an inductive union over closed discrete singular sets. It establishes structural and topological properties, including decomposition for f…
The note develops aspects of duality for constructive locally convex spaces, using previously introduced constructive notions of boundedness, continuity, and locally convex structure. It constructs a normal fundamental system of bounded sets for any such space, defines continuous and quasicontinuous…
The paper studies the asymptotic distribution of the maximum of a homogeneous process with independent increments, positive jumps, and negative drift, under analytic conditions on its spectral function. Using properties of the Laplace exponent, roots of the equation defining its analytic branches, a…
This paper studies extremal problems for real algebraic polynomials of degree n bounded by one on the interval [0,1], asking which polynomials maximize the real or imaginary parts of ordinary and angular derivatives at a prescribed point of the complex plane. The argument formulates these quantities…
The paper develops a classification of functions of several variables in weighted Lebesgue spaces by the rate of their best polynomial approximation on a cube. It defines strongly analytic, strongly entire, strongly quasianalytic, and strongly quasientire classes through geometric decay conditions o…
The paper addresses whether a meromorphic function of finite order must have a deficient value of maximal deficiency as an asymptotic value, a property known in certain entire-function cases. It gives a negative answer by constructing, for every order greater than one including infinite order, merom…
This note refines an asymptotic expansion in the central limit theorem for sums of independent identically distributed random variables with finite moment of integer order k at least 3 and a nonlattice type characteristic function condition. It proves a uniform weighted remainder estimate for the di…
This paper studies an initial boundary value problem for a nonlinear system of partial differential equations arising in meteorology, involving horizontal velocity components and a pressure dependent potential function. Under analyticity assumptions in the horizontal variables and uniform majorant c…
This note studies rational points over a number field on higher genus algebraic curves that admit several mappings to a common elliptic curve. It gives two approaches: one using Tate heights to prove eventual linear independence of the image points under independent mappings, and another using the d…
The paper studies the high energy asymptotic behavior of the spectral function for singular self-adjoint differential operators of even order 2m on the line and half-line. Using the parabolic equation associated with the operator, resolvent kernel estimates for truncated coefficients, and Tauberian …
The paper develops an operational calculus and Paley-Wiener type results for a connected semisimple complex Lie group, using the Fourier transform associated with elementary representations. It analyzes finite-dimensional projections of the algebra of generalized functions concentrated at the identi…
This paper studies value distribution for entire polyanalytic functions represented as finite polynomials in the conjugate variable with entire analytic coefficients, asking how far Picard-type theorems extend beyond the analytic case. It first proves a fundamental-theorem-of-algebra analogue for po…
This paper develops structural results on polyvectors, especially k-vectors expressible as sums of simple exterior products with all component covectors linearly independent. It proves uniqueness of such decompositions for k greater than 2, gives criteria for recognizing simple-type polyvectors, and…
This note studies the local structure of continuous strong Markov processes on a locally compact space through additive martingale-type functionals, called M-functionals. It develops quadratic variation and covariation for these functionals, proves absolute continuity relations between them, constru…
This note studies the minimaxity of Hotelling’s T squared test for testing a zero mean vector in a multivariate normal sample against alternatives with fixed Mahalanobis signal energy. Building on the reduction of Giri, Kiefer, and Stein, the authors treat the case p equals 2 and N equals 4 by trans…
The paper studies linear functionals on the Banach space of functions analytic in the unit disk and continuous on its closure. Using the Riesz representation theorem, the F. and M. Riesz theorem, and a generalized Riesz equality, it gives a unique decomposition of the dual space into discrete measur…
This paper classifies the possible nonoscillatory asymptotic behaviors of solutions to the second order linear equation with real continuous coefficients and sign definite coefficient q(t). Using a fundamental system consisting of a nonminimal positive solution and a minimal positive solution, the c…
The paper continues the study of surface parabolic potentials and fractional powers of parabolic operators in weighted Hölder spaces of functions with exponential growth. It proves a kernel cancellation lemma, boundedness of surface potential operators, and mapping properties for fractional integrat…
The paper extends a generalized area theorem for nonoverlapping simply connected domains to systems of functions mapping finitely connected domains conformally onto pairwise disjoint domains. Using Green functions, auxiliary kernel functions, and an area computation for the image of the complementar…
This paper continues the study of generalized solutions to first-order nonlinear Cauchy problems of the form \(u_t+f(u_x)=0\), under convexity assumptions on \(f\). It develops construction methods for such solutions, chiefly through vanishing viscosity approximations, and proves convergence estimat…
The paper studies bounded analytic operator functions on the unit disk with values in a separable Hilbert space, subject to contractivity, invertibility at the origin, and trace class perturbation conditions. It extends Potapov type multiplicative factorization to this infinite dimensional trace cla…
The paper studies triples of normally embedded Banach spaces and introduces notions of relatedness and absolute relatedness in terms of continuous normal scales and the index of an intermediate space. It proves lemmas reducing relatedness and absolute relatedness to the behavior of maximal and minim…
This paper studies approximation of periodic functions by bounded semiadditive operators, with emphasis on deriving smoothness properties from operator representations and estimating approximation orders when smoothness is measured by moduli of smoothness. It establishes a series of direct and inver…
The paper examines how to define solutions of nonlinear integral equations whose operators are discontinuous in the unknown function, noting shortcomings of earlier definitions when related to differential equations and continuation results. It proposes a new solution concept based on essential lowe…
This paper studies Orlicz classes and spaces generated by functions depending on both the point and the argument, on an arbitrary sigma-finite measure space. It formulates conditions, especially generalized growth conditions of Delta type, under which the Orlicz class and space coincide, mean conver…
This paper studies the asymptotic probabilities of first and second kind errors in Neyman Pearson testing between two hypotheses on the spectral density of a zero mean Gaussian stationary process observed at finitely many equally spaced points. For cases where the corresponding Gaussian measures are…
