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 develops homology and cohomology theories for infinite locally finite complexes using chains and cochains defined relative to a pair of coefficient groups, interpolating between the usual theories based on finite and infinite chains. It introduces topologies and compact completions for the…
This paper computes the Plancherel measure for zonal spherical functions on the Siegel upper half-plane, viewed as the symmetric space associated with the real symplectic group. It describes the relevant Cartan and nilpotent subgroups, derives an integral representation for the spherical functions, …
This note studies generally multivalued linear operators between separated locally convex spaces through their graphs, closures, openness, continuity, and adjoints. It establishes criteria relating openness and closedness of an operator to the behavior of its closure, range, kernel, and adjoint, inc…
This note studies nondegenerate inverse and direct spectra of locally convex spaces, with emphasis on relations between a spectrum and its strong dual conjugate spectrum. It proves nondegeneracy results for conjugate spectra under standardness and semireflexivity assumptions, and gives a necessary a…
This paper proves that every continuous decomposition of an n-dimensional ball into pairs of points has at least one degenerate element when n is at most 3, with the argument given for the three-dimensional ball and applicable to lower dimensions. Assuming a decomposition strictly into two-point ele…
This note studies the group of divisor classes of degree zero for the function field over the rationals defined by the Fermat quartic \(x^4+y^4=1\). The argument relates the genus 3 Jacobian of the complex curve to the product of three elliptic Jacobians arising from quadratic subfields, using norm …
This note studies spaces of holomorphic functions on domains in several complex variables, focusing on their topological isomorphism classes and Kolmogorov approximative dimension. Using nuclear space methods, unconditional bases, and Köthe sequence space representations, it gives explicit isomorphi…
The paper studies Korovkin-type systems for convergence of sequences of linear positive operators from the space of continuous functions on a compact set into bounded functions. It characterizes such systems by uniqueness of positive linear functionals and equivalently by a geometric condition on th…
This paper presents a finite monotone algorithm for a generalized linear programming problem arising in Kantorovich’s model of production planning: maximizing, over a polyhedron defined by linear inequalities, the minimum of several linear forms. The method gives a geometric construction in which su…
This paper studies the Dirichlet problem with zero boundary data for second order quasilinear elliptic equations in a strictly convex planar domain with smooth boundary. It establishes sufficient solvability conditions expressed through ellipticity, monotonicity or growth assumptions on the coeffici…
This paper studies the angular and logarithmic distribution of integer or lattice points on norm-defined curves and surfaces arising from quadratic and cubic number fields. It proves asymptotic formulas, with explicit error terms, for points on ellipses and hyperbolas of the forms associated with bi…
The paper estimates the error of a finite difference net method for the third boundary value problem for harmonic functions in a plane domain with sufficiently regular boundary and positive boundary coefficient. It constructs a difference Green function for the discrete problem, studies its boundary…
This note develops a continuous moment problem for Hilbert spaces of square integrable functions with respect to nondecreasing measures, extending earlier work on Hilbert, Bessel, and Riesz kernels. It gives sufficient, and in a stated setting necessary, boundedness conditions under which a prescrib…
The paper proposes an axiomatization of uniform spaces based on systems of subsets containing arbitrarily small members, called systems with small sets. It introduces majorization, regular subsystems, and cofinality, then formulates axioms intended to characterize such systems, including a separatio…
This paper gives an axiomatic characterization of semigroups embeddable in generalized groups, equivalently semigroups representable by partial one-to-one transformations. It introduces stable quasi-order relations and the strong quasi-order relation, proves that embeddability is equivalent to this …
This paper studies linear methods for summing Fourier series of periodic summable functions, defined by triangular matrices of multipliers. It proves a general bound for the associated kernels and derives necessary and sufficient conditions under which the transformed Fourier polynomials converge to…
This note extends the spectral theory of stationary random processes to homogeneous random fields on noncommutative groups and homogeneous spaces. Using the representation theory of separable locally compact groups of type I, it formulates analogues of Bochner’s theorem in which continuous positive-…
The paper studies a Poincaré boundary value problem for analytic functions in the unit disk, involving the real part of a linear expression in the function and its derivative on the boundary. Under the assumption that a transformed coefficient has only finitely many negative Fourier terms, the probl…
The paper studies the problem of extending a polynomial by adding higher degree terms so that all roots of the resulting polynomial lie on the unit circle. Using Newton’s formulas, the problem is reduced to representing the first power sums of inverse roots by points of modulus one, and a constructi…
This note studies rigidity under continuous bendings for surfaces of positive Gaussian curvature with boundary, using the Gauss, Peterson, Codazzi equations in isothermal coordinates and the associated function determined by the second fundamental form. By deriving a uniformly elliptic equation for …
The paper extends a theorem of N. M. Korobov on completely uniformly distributed sequences and normal digit sequences. It proves that, for a completely uniformly distributed sequence of real numbers, the two digit sequences obtained by taking the first base \(q_1\) digit and then the first base \(q_…
This paper establishes sharp Bernstein and Markov type estimates for the derivative of a trigonometric polynomial of order n bounded by one on an interval shorter than its period. The argument introduces explicit extremal trigonometric polynomials defined through a change of variables to algebraic p…
This note studies how the smoothness of boundary data for the planar Dirichlet problem determines the differential properties of the corresponding harmonic function in domains whose boundaries are piecewise smooth and have nondegenerate angles. Using Nikol’skii type function classes, it establishes …
The paper studies bounded regular functions on the complement of a closed subset of the extended complex plane through a duality framework involving analytic functions on the closed set and measures supported in the complement. It introduces a seminorm defined by minimal total variation of measures …
This note studies the flexibility and rigidity of general convex surfaces homeomorphic to an open disk, bounded by a simple closed curve, within the class of all convex surfaces. Using Alexandrov’s gluing theorem and Pogorelov’s uniqueness theorem, the problem is reduced to the existence of nontrivi…
This paper studies ordinary linear differential equations with small coefficients multiplying the highest derivatives near an irregular singular point of first rank at infinity. It constructs normal formal solutions associated with the roots of the characteristic equation, distinguishes those that h…
This note studies weighted polynomial approximation of analytic functions in unbounded domains, building on earlier completeness results for angular regions. For functions analytic in the upper half-plane with prescribed growth bound M(r), it proves an estimate for the best weighted polynomial appro…
This paper studies p-groups that can be decomposed as semidirect products of cyclic subgroups, equivalently groups with an invariant series of cyclic factors complemented in the group. It derives structural conditions on the defining conjugation relations, describes commutator subgroups and lower ce…
This paper introduces the notion of a normal scale of Banach spaces, replacing the analyticity condition used in earlier analytic scales by logarithmic convexity of norms with respect to the parameter. It gives basic structural properties of such scales, discusses admissible renormings and completio…
This note studies global well-posedness for constant-coefficient differential equations, or polynomial systems, of the form p(i∂/∂x)u = w, under the assumption that the polynomial has no zeros on the real manifold. It introduces the genus of the equation, defined through zero-free complex tubular do…
This paper constructs an external radical for automorphism groups of groups satisfying the maximal condition, modeled on the radical of an endomorphism ring. Using commutator series, nilautomorphisms, and passage to the holomorph, it proves criteria for external nilpotence, shows that the radical co…
This paper addresses Ponomarev’s question on whether a monotone mapping between spaces can be extended to a monotone mapping between bicompact extensions. It proves that if a monotone mapping from a completely regular space onto a normal space is open or closed, then any extension to a bicompactific…
This note addresses the relationship between three topological dimensions, covering dimension, small inductive dimension, and large inductive dimension, for locally bicompact groups. Building on paracompactness and known local product structure, it first reduces the equality of covering and small in…
This note studies conditions under which stable and locally stable groups of automorphisms are nilpotent or locally nilpotent, extending earlier results on automorphism groups admitting invariant stable series. Using commutator identities, properties of nil-automorphisms, and reductions to induced a…
This note studies singularities of analytic 1-fields defined as analytic sections of the projectivization of a complex analytic vector bundle, using a local formulation over open subsets of complex Euclidean space. It establishes criteria and constructions relating such fields to holomorphic section…
This paper applies the method of moduli to quasiconformal mappings in three-dimensional space. It proves a spatial analogue of the Grötzsch, Teichmüller extremal lemma for families of surfaces in a ball and uses it to derive distortion estimates for normalized quasiconformal self-mappings of the bal…
This note compares two analytic approaches to small solutions and bifurcation for nonlinear integral equations depending on a parameter: the Lyapunov, Schmidt method and the Nekrasov, Nazarov method. For an equation whose linear part has 1 as a simple eigenvalue, the paper formulates the correspondi…
This note studies when an isomorphism between the lattices of finitely generated submodules of free unitary modules over regular rings is induced by a corresponding semilinear mapping of the modules. Extending methods of Baer, it proves that for regular rings and rank at least three, an isomorphism …
This paper studies boundary value problems for a class of invariant first order elliptic systems with constant coefficients, formulated in terms of covariants and the exterior differentiation operators d and δ. The argument uses the invariant structure by doubling a smooth bounded Euclidean domain a…
This paper studies approximation of summable functions of two variables by the Riesz-Bochner means of their Fourier integrals, assuming that the circular mean of the function satisfies a Lipschitz condition of order alpha. Using the Bessel function representation of the Riesz-Bochner operator and es…
This paper introduces classes of multivariable functions defined through the convergence properties of their Haar series, denoted \(S_p\), and studies their basic normed-space structure and continuity behavior. It also defines classes \(H_\alpha\), multidimensional analogues of Lipschitz classes bas…
This note studies the distribution, over residues modulo a prime p, of very short exponential sums of the form \(\sum_{x=0}^{h}\exp(2\pi i ag^x/p)\), where \(g\geq 2\) is fixed and \(h\) grows but remains at most one half of \(\log p/\log g\). Using Markov’s method of moments, it computes the limiti…
This paper studies generalized left rings of quotients of an associative ring with respect to a multiplicatively closed system, especially the system complementing a proper prime ideal. It establishes technical extension and contraction criteria for left ideals, then applies them to the generalized …
This note studies nonclassical boundary value problems for partial differential equations using energy inequalities in Sobolev and negative norm spaces. It formulates correctness of boundary conditions through paired estimates for an operator and its formal adjoint, then develops an integration by p…
The paper studies a class of Sobolev-type systems of partial differential equations for which the Cauchy problem is well posed despite not belonging to the classical Kovalevskaya framework. It formulates a mixed problem with initial conditions imposed on solenoidal vector fields and boundary conditi…
This paper studies groups in which cyclic subgroups of specified prime orders are complemented, introducing primitive pi-factorizability and related notions of complete approximability by completely primitive finite groups. It gives structural characterizations in terms of embeddings into complete d…
The paper studies Fourier transforms of rapidly decreasing smooth functions on a connected complex semisimple Lie group using representations realized in topological spaces of homogeneous smooth functions on the basic affine space. It defines the basic group ring under convolution and identifies the…
This note studies when the root subspaces of a dissipative operator in a separable Hilbert space form a basis, extending earlier results on eigenvector bases. It develops criteria for sequences of subspaces to be Riesz or Bari bases, using separation, quadratic closeness to an orthogonal basis, and …
This note describes a “direct method” for proving embedding theorems by elementary integral estimates, using free parameters, dimensional considerations, differential order, and integral representations of powers of functions. It introduces definitions of dimension, additivity, and differential orde…
This paper studies connected compact Lie groups acting transitively on selected homogeneous manifolds, extending the known classification for spheres. It develops a topological method based on real cohomology, primitive elements, Poincaré polynomials, and ranks of homotopy groups, showing that certa…
