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 representations of the group of complex unimodular second order matrices, identified with the Lorentz group setting, that are unitary in spaces with an indefinite Pi_n metric. It reduces the classification problem to representations possessing a maximal null invariant subspace and …
This note determines the sharp perturbation bound in the Paley, Wiener problem for exponential systems in \(L_2(-\pi,\pi)\). For real frequencies \(\lambda_k=k+\delta_k\), it proves that if \(\sup_k|\delta_k|<0.25\), then \(\{e^{i\lambda_k t}\}\) is a Riesz basis, using the Paley, Wiener lemma and F…
This note studies double layer potentials carried by a general closed oriented hypersurface in multidimensional Euclidean space, using the solid angle measure induced by projection from a point onto the unit sphere. It gives criteria for this set function to extend to a finite generalized Borel meas…
This paper studies admissible infinitesimal bendings of a class of nonregular developable surfaces called ribbed cylindroids of type A, whose regular zero Gaussian curvature parts are joined along generator ribs and whose boundary curves lie in parallel planes. Using a lemma on infinitesimal bending…
This paper studies infinitesimal deformations of positively curved surfaces with prescribed changes of the linear element when the boundary is constrained to slide along a supporting surface. The problem is reduced to a boundary value problem for functions derived from the displacement field, and so…
This note addresses the reduction principle for stability of the zero solution of a nonlinear differential system whose linear part has critical variables with zero real eigenvalues and stable variables with negative real eigenvalues. Under local Lipschitz assumptions with an infinitesimal constant,…
This paper studies when functions continuous on an unbounded closed set in the complex plane, and analytic at its interior points, can be uniformly approximated on that set by entire functions. It proves that such approximation is possible for every admissible function exactly when the set satisfies…
The paper studies when generalized solutions of differential equations in a half-space possess boundary limits as the normal variable tends to zero. It introduces spaces measuring the existence of such limits for distributions and proves regularity results for systems solvable with respect to the hi…
This note studies a nonlinear singular integral equation with Cauchy kernel in a Hölder-type class of functions that vanish at the endpoints of a finite interval with prescribed power behavior. Under a Lipschitz condition on the nonlinearity, the authors prove mapping and continuity properties for t…
This paper develops the theory of smooth oriented codimension one foliations on orientable manifolds, extending earlier work on closed leaves and Reeb components in three dimensional manifolds. It introduces limit epimorphisms for homotopy classes in leaves and proves that certain global topological…
The paper studies weight characteristics of topological spaces satisfying natural invariance, monotonicity, additivity, and nontriviality conditions, and introduces local, modular, unimodular, and stepwise weight functions. It proves that local characteristic functions on regular spaces are stepwise…
The paper studies the construction of topologically reflexive KB-spaces within the framework of semi-ordered spaces, starting from an arbitrary KB-space and its maximal extension. It defines spaces \(X_p\) by requiring the p-th power of the modulus to belong to the original space, proves that these …
The paper studies limit functions of uniformly convergent sequences of linear aggregates built from an entire function and its generalized derivative structure, extending earlier results for exponential systems and related functions. For entire functions defined by coefficients involving an auxiliar…
The paper studies the distribution of values of an irreducible monic polynomial with integer rational coefficients whose prime divisors are all at most a parameter z. It reduces the problem to factorization of linear factors in the normal algebraic number field generated by the polynomial and combin…
The paper studies spectral functions and generalized resolvents of closed isometric operators in Hilbert space, extending ideas previously developed for symmetric and Hermitian operators. It gives intrinsic necessary and sufficient conditions for a family of bounded operators to be the generalized r…
This note studies conjugate functions of two variables and the summability behavior of the corresponding double conjugate trigonometric series. It addresses whether one dimensional results of Riesz, Zygmund, Kinukawa, Turán, and Marcinkiewicz and Zygmund extend to multiple Fourier series, using coun…
This paper studies properties of tau-polynomials, defined as functionals on a space of piecewise continuous trajectories whose sufficiently high tau-derivative vanishes. It develops a decomposition of polynomial densities into simple and degenerate parts relative to a fixed trajectory, leading to a …
The paper studies the growth and asymptotic distribution of eigenvalues of a linear integral equation on the unit interval under different regularity assumptions on the kernel. For kernels analytic in the second variable in a domain touching the endpoints and satisfying prescribed endpoint growth bo…
This paper studies homotopy groups of spaces of smooth embeddings of the circle into spheres and Euclidean balls, extending the usual classification problem from path components to higher homotopy groups. Using fibrations defined by fixing a tangent vector, polygonal models for embedded arcs, spectr…
This paper studies unitary representations of adele groups associated with linear algebraic groups over number fields, with particular emphasis on the action of an adele group on functions on the quotient by the principal adele subgroup. It constructs irreducible representations as restricted tensor…
The paper applies Krein’s method of directing functionals to pairs consisting of a closed symmetric operator with a finite system of directing functionals and a bounded operator that precommutes with it. It proves the existence of a self-adjoint extension of the symmetric operator and a norm-preserv…
The paper studies the geometric and spectral structure of the closed one-dimensional Schrödinger operator on the line with continuous complex-valued periodic potential. Using the family of operators with quasiperiodic boundary conditions on one period, it identifies the spectrum as the union of thei…
The paper studies commutative Banach algebras with one-dimensional radical annihilated by the whole algebra, focusing on the classification of algebraically decomposable cases with a prescribed semisimple quotient algebra. It introduces functionals on a space generated by products in the quotient al…
This note examines Kleene’s notion of realizability for logico-arithmetical formulas from a mathematical rather than semantic standpoint, focusing on how realizations are recorded. It defines a parallel notion of completion, structurally identical to realizability except that every completion has th…
This paper studies boundary-value problems for a broad class of singular integral and integro-differential equations in a bounded smooth domain, including elliptic differential equations as special cases. Using factorization of the homogeneous symbol at the boundary and Wiener-Hopf analysis in a hal…
The paper studies the existence and behavior of similar tests for the Behrens-Fisher problem with two independent normal samples and unknown means and variances, focusing on homogeneous nonrandomized tests depending on the sufficient statistics through the variables formed from the sample mean diffe…
This note studies the spectral properties of regular quasi-differential operators in L2(a,b), generally non-self-adjoint, defined by a self-adjoint quasi-differential expression and linearly independent boundary conditions. It introduces a normalized Wronskian determinant formed from solutions satis…
The paper studies the asymptotic behavior of a discrete dynamic programming problem with a continuous convex state space, continuous transition income, and terminal payoff. It proves that the optimal value grows linearly up to a bounded error, identifies the growth rate with the supremum of average …
The paper develops a theory of singular elliptic equations and systems whose symbols have variable order on closed manifolds and bounded domains with smooth boundary. It introduces Sobolev-type spaces of variable smoothness, proves compact embedding properties, and establishes Fredholm, or Phi-opera…
The paper studies how the nil-element spaces and core spaces associated with the closed operator pencil A minus lambda I in a Banach space vary with the complex parameter lambda on the Fredholm-type set where the range is closed and one of the nullity or defect numbers is finite. Using analytic repr…
The paper extends Nevanlinna’s parametric representation theorem for meromorphic functions of bounded characteristic in the unit disk to a one-parameter family of broader classes. Using Riemann-Liouville fractional integrals and derivatives, it defines an alpha-characteristic for meromorphic functio…
This paper studies solvability and uniqueness for hypoelliptic equations in the whole space, focusing on how radiation-type conditions at infinity select fundamental solutions. It introduces integral-form conditions equivalent to previously used pointwise asymptotic conditions, proves a limiting abs…
This paper studies the one-dimensional Schrödinger equation with a real periodic potential under a real nonperiodic perturbation that decays sufficiently fast at infinity. It addresses when such a perturbation can introduce only finitely many discrete eigenvalues into each gap of the continuous spec…
This paper studies stationary resonance regimes in one degree of freedom oscillatory systems with slowly varying parameters and a small nonlinear perturbation that is periodic in time. Using variables defined by the extrema and phase of the unperturbed motion, the authors derive averaged equations n…
This note studies the determination of principal indices of Laurent series convergent in an annulus, extending earlier criteria known for polynomials and related sufficient conditions. The authors introduce transformed Laurent series formed from products over roots of unity and define coefficient ra…
This paper develops a theory of singular integral equations on an infinite multidimensional cylinder, modeled as a strip with periodic variables and unbounded Euclidean variables. It introduces an appropriate Fourier transform, constructs periodic singular kernels in the Calderón and Zygmund setting…
This note studies asymptotic equivalence between solutions of an almost linear system x' = Ax + F(t,x) and its associated linear system y' = Ay, where the perturbation satisfies a Lipschitz bound with time-dependent coefficient g(t). It introduces a notion of deviation between solution vectors and s…
This paper studies a two-layer thermoconvective boundary value problem motivated by heat propagation in a reservoir under thermal injection, with vertical heat conduction in both layers and horizontal convection in one layer. After a change of variables, the problem is formulated through Green funct…
This paper studies inverse spectra and classes of Hausdorff spaces characterized by mappings subordinate to open covers, especially omega-mappings and weak omega-mappings. It proves dimension-preserving factorization and spectral representation results, showing, for example, that normal finite-dimen…
The paper develops an approximate method for solving a class of linear singular integral equations arising in dispersion-relation problems, in particular equations of Chew-Low type for pion-nucleon processes. It first establishes a sufficient smallness condition under which successive approximations…
This note studies how the growth of an entire function along a fixed ray compares with its Nevanlinna characteristic. Building on examples showing that the corresponding upper limit may be infinite, it proves a sharp upper bound for the lower limit of the ratio of the logarithm of the function on th…
This note develops an analogue of the spectral projector function for self-adjoint operators with real spectrum in a Pontryagin space with indefinite metric. It defines spectral functions with finitely many critical points, introduces the index, order, and associated subspaces of such points, and pr…
The paper studies irreducible B-spaces, Riemannian spaces with a covariantly constant symmetric affinor, in the case where the affinor has a single real eigenvalue and equal Jordan block sizes. Using canonical coordinates and differential relations among the metric and powers of the affinor, it show…
This paper extends necessary optimality conditions for control problems from finite-dimensional settings to systems evolving in Banach spaces. For equations with measurable controls and endpoint constraints, including fixed endpoints, terminal manifolds, and terminal convex bodies, it formulates ass…
This paper studies integral representations of continuous linear functionals on spaces of functions harmonic or analytic in the interior of a Jordan curve and continuous on its closure. It relates representing measures in the domain to boundary measures via harmonic measure, gives criteria for when …
This note proves energy inequalities with boundary norms for elliptic differential operators whose coefficients may be discontinuous across an interior interface. The authors formulate general boundary conditions on the exterior boundary and conjugation conditions on the discontinuity surface, intro…
This note studies Weierstrass-type approximation in Banach spaces of infinitely differentiable functions whose derivatives are controlled by a logarithmically convex sequence. It proves that, under the stated growth assumptions, the closure of entire functions of exponential type, and in the periodi…
