Showing 50 of 5847 papers in Mathematics

UNIFORM APPROXIMATIONS BY RATIONAL FUNCTIONS (ALGEBRAIC AND TRIGONOMETRIC) AND GLOBAL FUNCTIONAL PROPERTIES

E. P. Dolzhenko
1966 SovietRxiv: ru-196601.93069

This paper studies how the rate of uniform approximation of a function by algebraic or trigonometric rational functions controls global regularity properties expressed through generalized variation, generalized absolute continuity, and Orlicz space moduli. Using estimates for the Phi-variation and O…

THE FIRST BOUNDARY-VALUE PROBLEM

V. R. Portnov
1966 SovietRxiv: ru-196601.92861

The paper studies the first boundary-value problem for a class of differential equations and systems in function spaces more general than weighted or unweighted Sobolev spaces, whose polynorms include both derivatives and differential expressions. It formulates geometric and weight conditions on pos…

ON CONJUGATE FUNCTIONS

L. V. Zhizhiashvili
1966 SovietRxiv: ru-196601.92817

This paper studies conjugate functions associated with periodic summable functions and the regularity of integral transforms built from them. For even one variable functions, it establishes continuity and uniform convergence results for transforms defined through the conjugate function, including a …

POSITIVE MIXED PROBLEMS

M. S. Agranovich
1966 SovietRxiv: ru-196601.92600

This note studies mixed initial-boundary value problems in a cylindrical domain for general first-order hyperbolic systems whose coefficients need be Hermitian only on the lateral boundary. Under generalized Petrovskii hyperbolicity, a noncharacteristic boundary condition, and Friedrichs-type positi…

INFINITESIMAL BENDINGS OF SURFACES OF REVOLUTION OF POSITIVE CURVATURE WITH A CONICAL OR PARABOLIC POINT AT THE POLE

L. G. Mikhailov, Z. D. Usmanov
1966 SovietRxiv: ru-196601.92520

The paper studies infinitesimal bendings of surfaces of revolution with positive curvature when the pole is a conical or parabolic singular point. It develops a reduction of a first order generalized Cauchy, Riemann type system with singular coefficients to a second order elliptic equation, then app…

ASYMPTOTICS OF EIGENVALUES AND EIGENFUNCTIONS OF ONE-DIMENSIONAL SINGULAR DIFFERENTIAL OPERATORS

M. V. Fedoryuk
1966 SovietRxiv: ru-196601.92258

This paper studies asymptotic properties of solutions, spectra, and eigenfunctions for one-dimensional singular differential systems of the form y' equals mu A(x)y under structural and regularity assumptions on the matrix coefficient at infinity. It proves a fundamental matrix asymptotic expansion f…

EMBEDDING THEOREMS FOR FUNCTIONS DEFINED ON UNBOUNDED DOMAINS, AND THEIR APPLICATION TO BOUNDARY-VALUE PROBLEMS FOR THE POLYHARMONIC EQUATION

T. S. Pigolkina
1966 SovietRxiv: ru-196601.91885

The paper studies embedding theorems for weighted Sobolev type spaces of functions defined on unbounded Euclidean domains, including half-spaces and traces on lower-dimensional hyperplanes. It defines appropriate weighted norms, including fractional-order variants, establishes several trace and embe…

On Gaussian Linear Functionals on a Countably Hilbert Space

Unknown
1966 SovietRxiv: ru-196601.91874

This paper studies Gaussian probability measures on the space of continuous linear functionals over a real separable countably Hilbert space. It characterizes the possible mean and covariance functionals, showing that they arise from a continuous linear form and a positive nuclear operator with resp…

ON FINITE GROUPS WITH A GIVEN SYLOW 2-SUBGROUP

V. D. Mazurov
1966 SovietRxiv: ru-196601.91829

This paper studies finite groups whose Sylow 2-subgroups have a specified presentation and relates them to earlier classification results of Gorenstein and Walter. It proves that if the centralizer of a distinguished involution in such a group is soluble, then the group has one of three described st…

TOPOLOGY OF FUNCTION SPACES

S. I. Alber
1966 SovietRxiv: ru-196601.90421

This paper studies topological properties of function spaces arising in the variational theory of closed geodesics, focusing on spaces of unoriented loops and unoriented closed paths on Riemannian manifolds diffeomorphic to spheres. Using a grading of homology groups by critical values of the length…

Maximal and Normal Series of Finite Groups

L. Ya. Polyakov
1966 SovietRxiv: ru-196601.90232

This note studies how structural relations among maximal subgroups of a finite group constrain its normal structure, especially nilpotency, solvability, and supersolvability. It proves that quasireachability or permutability conditions on first through fourth terms of maximal series force strong res…

AN EXISTENCE THEOREM FOR THE SOLUTION OF THE PROBLEM OF SHORT-RANGE WEATHER FORECASTING

G. V. Demidov, G. I. Marchuk
1966 SovietRxiv: ru-196601.90164

The paper proves a local existence theorem for a smooth solution of a mixed initial boundary value problem for a quasilinear system modeling aspects of short-range weather forecasting in a domain unbounded in the horizontal variables. The solution is constructed by the method of fractional steps, re…

Structural method for determining dimensionality

Unknown
1966 SovietRxiv: ru-196601.90021

This paper develops a structural approach to dimension by first defining dimension for partially ordered sets in terms of chains of filters, then applying this notion to basic lattices of closed sets in topological spaces. It proves that zero-dimensional distributive lattices with zero and unit are …

ON A CLASS OF OPERATORS

M. G. Krein, Yu. L. Shmul'yan
1966 SovietRxiv: ru-196601.89542

The paper studies bounded linear operators in Hilbert spaces equipped with an indefinite metric, focusing on plus-operators, \(J\)-noncontracting operators, and their adjoints. It develops an elementary theorem on Hermitian sesquilinear forms and applies it to show when plus-operators are collinear …

ON THREE LINEARIZED INVERSE PROBLEMS FOR HYPERBOLIC EQUATIONS

M. M. Lavrent'ev, V. G. Romanov
1966 SovietRxiv: ru-196601.89422

This paper formulates and analyzes three linearized inverse problems for hyperbolic equations arising from wave propagation. The first concerns recovery of a refractive coefficient from boundary travel times, and in a special background medium it is reduced to determining a perturbation from its int…

ON SOME PROPERTIES OF ALGEBRAS OF CONTINUOUS FUNCTIONS

E. L. Arenson
1966 SovietRxiv: ru-196601.89393

This note studies closed subalgebras of the algebra of continuous complex functions on a compact Hausdorff space, focusing on antisymmetry, weak analyticity, and partitions associated with such algebras. It introduces antisymmetric measures and sets of weak analyticity, proves reconstruction criteri…

A SUBGROUP CHARACTERIZATION OF SOME FINITE GROUPS

Ya. G. Berkovich
1966 SovietRxiv: ru-196601.89094

This note studies how structural and embedding properties of selected subgroups determine the structure of finite groups. It formulates a series of classification results for groups whose maximal, higher maximal, or maximal solvable subgroups satisfy restrictions such as being minimal nonnilpotent, …

EXTREMAL PROBLEMS IN THE THEORY OF POLYNOMIAL OPERATIONS

D. L. Berman
1966 SovietRxiv: ru-196601.88672

This paper studies extremal norm problems for linear polynomial operations on translation-invariant spaces of periodic functions, especially continuous and integrable periodic functions. For convolution-type operations determined on trigonometric polynomials of order at most n by a kernel, the paper…

ON MEASURES IN LINEAR SPACES

G. E. Shilov
1966 SovietRxiv: ru-196601.88627

This paper studies when a premeasure defined on cylindrical sets in a real linear space can be extended to a countably additive measure without assuming a topology on the space. It proves that, when the chosen linear functionals separate points, such an extension exists exactly when the image of the…

HYPERSCALES OF BANACH STRUCTURES

S. G. Krein, Yu. I. Petunin, E. M. Semenov
1966 SovietRxiv: ru-196601.88340

This paper develops the notion of hyperscales of ideal Banach function structures within the setting of measurable functions ordered almost everywhere. It defines hyperscales by a logarithmic convexity type inequality, establishes existence and properties of maximal hyperscales, and proves interpola…

ON FIELDS ASSOCIATED WITH ENVELOPING ALGEBRAS OF LIE ALGEBRAS

I. M. Gel'fand, A. A. Kirillov
1966 SovietRxiv: ru-196601.87925

This note studies skew fields of fractions associated with universal enveloping algebras of Lie algebras over a field of characteristic zero, motivated by noncommutative rings arising in analysis. It introduces a dimension invariant for arbitrary fields over a base field, proves that filtered algebr…

On the Diameter of a Strongly Connected Graph

Unknown
1966 SovietRxiv: ru-196601.87626

This paper studies lower bounds for the diameter of finite strongly connected directed graphs in terms of the number of vertices and the cyclomatic number. Building on a known radius inequality, it proves that for any such graph with cyclomatic number at least two, the product of the diameter and th…

SOME CRITERIA FOR THE COMPLETENESS OF A SYSTEM OF ROOT VECTORS OF A LINEAR OPERATOR IN A SPACE WITH TWO NORMS

I. A. Novosel'skii
1966 SovietRxiv: ru-196601.87414

This note establishes criteria for completeness of systems of root vectors of completely continuous linear operators in a Banach space equipped with an additional weaker Hilbert norm. It extends Hilbert space completeness results to spaces with two norms, proving completeness theorems for perturbed …

SET-THEORETIC OPERATIONS

V. I. Amstislavskii
1966 SovietRxiv: ru-196601.87255

The paper develops a general framework for recursive hierarchies of length up to the least nonconstructive ordinal in an arbitrary space, using set-theoretic operations, bases, and effectively controlled numberings. It introduces standard operators on enumerated families of sets, defines recursive h…

ON THE DENSITY OF FINITE FUNCTIONS IN WEIGHTED SPACES

G. N. Yakovlev
1966 SovietRxiv: ru-196601.85793

The paper studies weighted Sobolev spaces on a bounded Lipschitz domain, where the weight depends on the distance to a smooth manifold that may lie on or inside the boundary. It formulates trace and zero boundary conditions according to whether a certain integral determined by the weight converges, …

AN EXACT INTERPOLATION THEOREM

V. A. Dikarev, V. I. Matsaev
1966 SovietRxiv: ru-196601.85739

This note studies whether the range conclusion in the Riesz-Thorin interpolation theorem can be sharpened from an ordinary Lebesgue space to a smaller rearrangement-invariant space. Using Lorentz-type spaces defined by decreasing rearrangements, the authors prove an interpolation theorem for operato…

ON QUASICONFORMAL MAPPINGS IN SPACE

A. V. Sychev
1966 SovietRxiv: ru-196601.85237

The note studies quasiconformal mappings in three-dimensional Euclidean space, with emphasis on distortion estimates for self-mappings of the unit ball and on extremal mappings of domains with edges. Using modulus estimates for ring domains and comparisons with planar extremal mappings, it derives H…

On Primary Ideals in the Space $\mathscr{L}(0,\infty)$

Unknown
1966 SovietRxiv: ru-196601.85072

The paper studies closed primary ideals in the convolution algebra of integrable functions on the positive half-line, using Fourier transforms on the closed lower half-plane and invariance under right shifts. It describes three cases: interior points yield a discrete chain of ideals defined by vanis…

DESCRIPTION OF COMPLETELY IRREDUCIBLE REPRESENTATIONS OF A SEMISIMPLE COMPLEX LIE GROUP

D. P. Zhelobenko, M. A. Naimark
1966 SovietRxiv: ru-196601.84663

This note studies the classification of completely irreducible representations of a connected semisimple complex Lie group in arbitrary complete locally convex spaces. It introduces notions of complete irreducibility and weak equivalence suitable for nonunitary representations, relates them to the c…

THE GRID METHOD FOR THE NAVIER–STOKES EQUATIONS

A. Krzhivitskii, O. A. Ladyzhenskaya
1966 SovietRxiv: ru-196601.84047

This paper presents two finite-difference schemes for the initial-boundary value problem for the incompressible Navier-Stokes equations in a bounded three-dimensional domain. The authors formulate an implicit grid method with discrete solenoidality, boundary and initial conditions, prove layerwise u…

ON A METHOD FOR INVESTIGATING NONLINEAR SINGULAR EQUATIONS

A. I. Guseinov, Kh. Sh. Mukhtarov
1966 SovietRxiv: ru-196601.83032

This note proposes a method for studying a nonlinear singular integral equation with Cauchy-type kernel in a weighted Hölder class introduced by Guseinov. It establishes a series of functional inequalities relating weighted Hölder norms and weighted \(L_p\) norms, then uses them to show that the ass…