Recent Papers

APPLICATION OF THE CONTOUR INTEGRAL METHOD TO THE SOLUTION OF MIXED PROBLEMS WITH BOUNDARY CONDITIONS OF MIXED TYPE

ON SPACES COABSOLUTE WITH METRIC SPACES

This paper studies topological spaces that admit perfect irreducible mappings onto metrizable spaces, equivalently in relation to coabsoluteness with metric spaces. It proves a characterization: such a single-valued mapping exists precisely when the space is a paracompact p-space containing a dense …

AUTOMORPHISMS OF ALGEBRAIC GROUPS

This paper studies rational automorphisms and subgroup structure in algebraic groups, focusing on invariant Cartan subgroups, unipotent Borel subgroups, and fixed point phenomena. It proves a global analogue of the Borel, Serre, and Mostow invariance theorem: finite supersolvable groups of rational …

PERTURBATION OF EIGENVALUES

This paper studies perturbations of eigenvalues and eigenelements of closed linear unbounded operators in a complex Banach space near a finite-dimensional eigenspace. Using projectors, solvability conditions for the associated nonhomogeneous equation, and a reduction to a finite homogeneous linear s…

Nonlinear integrals of potential type and their properties

STABILITY ON A FINITE TIME INTERVAL IN THE CASE OF ONE ZERO AND A PAIR OF PURELY IMAGINARY ROOTS

The Dirichlet problem for degenerate elliptic equations with nonlinear lower order terms

Corrections to the article “On a boundary value problem for a vector holomorphic in a half-space” (DAN, vol. 154, no. 2, 1964)

ON THE REDUCIBILITY OF LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS WITH QUASI-PERIODIC COEFFICIENTS

ON THE STABILITY OF STATIONARY SOLUTIONS OF A MIXED PROBLEM

The paper studies the large time behavior of solutions to a parabolic mixed boundary value problem arising from a model of chemical processes in a flat catalyst grain, focusing on a reduced scalar equation with nonlinear heat release. By analyzing stationary solutions through the associated nonlinea…

Bibliography of Journal Articles

This bibliographic notice compiled for the February 1966 issue of Differential Equations surveys recent journal articles from 1965 related to differential equations, integral equations, stability theory, boundary value problems, numerical methods, and mathematical physics. The entries list authors, …

On the 50th Anniversary of A. V. Bitsadze

This biographical survey marks the fiftieth anniversary of A. V. Bitsadze and reviews his scientific and pedagogical work in partial differential equations. It outlines his career from Tbilisi to the Steklov Institute and the Siberian Branch of the Academy of Sciences, then summarizes major contribu…

TRANSFORMATIONS OF WELL-POSED VARIATIONAL PROBLEMS

The paper studies transformations of variational optimal control problems for differential equations with compact control sets, focusing on when the original problem is well posed in terms of continuous dependence of endpoint control classes. It proves that, under this well-posedness condition, the …

ON RINGS OF OPERATORS IN A SPACE WITH INDEFINITE METRIC

This paper studies symmetric representations of rings with involution by bounded operators on spaces with indefinite metric of type Pi_n, extending invariant subspace results of Pontryagin and Naimark. Using decomposition lemmas for adjoint-closed operator families, a finite-dimensional perturbation…

ON ONE GENERALIZATION OF PERFECT MAPPINGS

The paper introduces n-perfect mappings as a generalization of perfect mappings, using Čech growths of finite order and the classes K_n to describe compactness type properties of point inverses and behavior at infinity. It states a series of theorems relating n-perfectness, closedness of successive …

ON THE APPROXIMATION OF CONTINUOUS AND DIFFERENTIABLE FUNCTIONS BY ALGEBRAIC POLYNOMIALS ON AN INTERVAL

The paper studies best uniform approximation of continuous and differentiable functions on an interval by algebraic polynomials, comparing it with known results for trigonometric approximation of periodic classes with prescribed moduli of continuity. It establishes asymptotically sharp lower and upp…

ON CONDITIONS FOR THE EXISTENCE OF THE GREEN’S FUNCTION OF A BOUNDARY VALUE PROBLEM

ON THE THEORY OF EXTREMAL PROBLEMS FOR QUASICONFORMAL MAPPINGS OF CLOSED RIEMANN SURFACES

This note studies extremal problems for quasiconformal homeomorphisms between closed Riemann surfaces of genus greater than one, in a fixed homotopy class and with bounded maximal dilatation, maximizing a real functional depending on the images of finitely many points. Using Teichmüller theory, vari…

TOWARD THE SOLUTION OF VARIATIONAL PROBLEMS OF NONCLASSICAL TYPE

The paper develops a method for treating variational and optimal control problems with inequality constraints on controls or coordinates by replacing the constrained quantities with trigonometric transformations, especially sine functions. This converts the nonclassical problem with one-sided variat…

ON THE UNIQUENESS OF SOLUTIONS OF PROBLEMS WITH FRANKL AND TRICOMI CONDITIONS FOR THE GENERAL LAVRENT'EV–BICADZE EQUATION

ON THE ASYMPTOTIC PROPERTIES OF THE RESOLVENT OF AN INTEGRAL EQUATION WITH A KERNEL DEPENDING ONLY ON DIFFERENCES OF THE VARIABLES

The paper studies the asymptotic behavior of the resolvent of an integral equation on expanding star-shaped domains, for kernels depending only on the difference of variables and satisfying Fourier-transform positivity and integrability assumptions. Using an orthogonal system adapted to the weighted…

RESTRICTION OF A REPRESENTATION OF THE COMPLEMENTARY SERIES OF THE COMPLEX UNIMODULAR GROUP OF SECOND ORDER TO A REAL SUBGROUP

This paper studies the restriction to the real unimodular subgroup of a complementary series representation of the complex unimodular group of order two, where the restricted representation is reducible. The analysis first treats the subrepresentation on functions supported in the upper half-plane, …

ON THE SIMULTANEOUS APPROXIMATION OF A FUNCTION AND ITS DERIVATIVES BY ALGEBRAIC POLYNOMIALS

This paper proves a theorem on simultaneous approximation of a function and its derivatives by algebraic polynomials on a finite interval. For functions with a continuous r-th derivative on [-1,1], it constructs an explicit polynomial of degree at most n whose derivatives up to order r approximate t…

Criterion for the Existence of a Bicompact Element in a Continuous Decomposition. Theorem on the Invariance of Weight under Open-Closed Finite-to-One Mappings

The paper proves two results in general topology concerning continuous decompositions and finite-to-one mappings. First, for a regular space with a symmetrix and a continuous closed map onto a T1 space, it shows that the range splits into a sigma-discrete exceptional part and a part over which all i…

ON QUASIANALYTIC CONTINUATION OF ANALYTIC FUNCTIONS THROUGH A JORDAN ARC

The paper studies quasianalytic continuation of analytic functions defined on two nonintersecting Jordan domains whose boundaries share an arc. It introduces classes of functions characterized by rational approximation with poles confined to derivable singular sets and by geometric rates of converge…

Corrections to the article “On the dimension of remainders in compact extensions” (DAN, Vol. 160, No. 3, 1965)

ASYMPTOTIC DISTRIBUTION OF EIGENFREQUENCIES OF A PLANE MEMBRANE IN THE CASE OF SEPARABLE VARIABLES

ANALYTIC STRUCTURE

ON THE ESTIMATION OF THE NON-OSCILLATION INTERVAL OF A DIFFERENCE EQUATION AND DIFFERENCE BOUNDARY VALUE PROBLEMS

This paper studies non-oscillation for an nth order linear difference equation on a finite mesh and related nonlinear difference boundary value problems. Using estimates for mesh functions with prescribed sign changes, based on convexity and extreme point arguments, it derives criteria for non-oscil…

Classification of irreducible unitary representations of the group of matrices of order two over a locally compact field

This note proves an exhaustion theorem for the irreducible unitary representations of the group of second order matrices over a disconnected locally compact nondiscrete field, focusing on the determinant one subgroup. It recalls the continuous, supplementary, special, discrete, and one dimensional d…

A METHOD FOR INVESTIGATING THE STABILITY OF SYSTEMS WITH AFTEREFFECT

The paper develops a Lyapunov based method for studying stability of differential systems with aftereffect, where derivatives depend on delayed state functions. By reversing time, the delayed system is associated with a system with advance, allowing the derivative of a positive definite function to …

ON A PROPERTY OF SOLUTIONS OF A PARABOLIC EQUATION

This note studies unique continuation properties for second order linear parabolic equations when the coefficients may depend on both time and one spatial variable. Extending a result of Ito and Yamabe for time-independent coefficients, it proves that a solution in a bounded space-time domain with z…

ON STATIONARY SOLUTIONS OF MIXED PROBLEMS ARISING IN THE STUDY OF CERTAIN CHEMICAL PROCESSES

This paper studies the multiplicity of stationary solutions for boundary-value problems arising in mathematical models of catalytic chemical processes. It reduces several parabolic and reactor models to nonlinear ordinary differential or integral equations, derives functional equations for determini…

BINARY ADDITIVE PROBLEMS WITH ERGODIC PROPERTIES OF SOLUTIONS

This note studies the distribution of solutions to the Hardy, Littlewood type equation p plus xi squared plus eta squared equals n, where p is prime and the integer point xi, eta is restricted to a growing planar domain inside the circle of radius square root n. Extending earlier asymptotic formulas…

ON A MINIMAX PROBLEM IN THE THEORY OF CUBATURE FORMULAS

This paper studies a minimax problem for cubature formulas by estimating the formula error as the norm of a continuous linear functional on weighted Hilbert spaces of generalized functions. Using Fourier transforms, the author derives extremal functions for the error functional in spaces defined by …

ON CERTAIN PROBLEMS IN THE ANALYTIC THEORY OF EQUATIONS OF THE FIRST KIND

ON THE QUESTION OF THE EXISTENCE OF SOLUTIONS OF DIFFERENTIAL AND INTEGRO-DIFFERENTIAL EQUATIONS HAVING ASYMPTOTIC PARABOLAS

ON THE QUESTION OF ISOMORPHISMS OF AN ANALYTIC SPACE COMMUTING WITH A POWER OF THE DIFFERENTIATION OPERATOR

The paper studies continuous isomorphisms of spaces of analytic functions in a disk and of entire functions that commute with a power of the differentiation operator. It shows by counterexample that earlier descriptions by Delsarte, Lions, and Viner do not give the full group for powers of order at …

Elliptic Operators and Submanifolds

This paper continues the authors’ work on elliptic operators associated with submanifolds, introducing a complex Kähler version of the trace construction and formulating its behavior in K-theory. It proves contravariant Riemann-Roch type formulas for the K-theoretic symbols of traced elliptic operat…

Regularization of Incorrect Problems for Equations of Mathematical Physics

ON LOCALLY NILPOTENT SUBGROUPS OF THE INFINITE SYMMETRIC GROUP

This paper studies locally nilpotent and nilpotent subgroups of the finitary symmetric group on an infinite set. Using representations of permutation groups on transitivity systems and centralizer arguments, it proves that every transitive locally nilpotent subgroup of the finitary symmetric group i…

GEOMETRIC THEORY OF UNITARY EQUIVALENCE OF MATRICES

This note studies unitary equivalence of finite sequences of complex matrices by translating the problem into the unitary geometry of orthogonal decompositions determined by eigenspaces of normal matrices. It first reduces arbitrary matrices to Hermitian components, then characterizes equivalence th…

ON MEASURABLE POLYLINEAR AND POWER FUNCTIONALS IN CERTAIN LINEAR SPACES WITH MEASURE

The paper studies measurable linear, polylinear, and power functionals on infinite product linear spaces equipped with product measures, and on the space of continuous functions with Wiener measure. It gives axiomatic definitions and proves uniqueness, representation, and completeness results, inclu…

EXISTENCE THEOREMS AND CONVERGENCE OF MINIMIZING SEQUENCES FOR EXTREMUM PROBLEMS IN THE PRESENCE OF CONSTRAINTS

The paper studies existence and convergence properties for constrained minimization problems in real Banach spaces, focusing on lower semicontinuous quasiconvex, strictly quasiconvex, uniformly quasiconvex, and strongly convex functionals. It proves weak lower semicontinuity of quasiconvex functiona…

ON THE ALGEBRAIC INDEPENDENCE OF VALUES OF \(E\)-FUNCTIONS SATISFYING LINEAR NONHOMOGENEOUS DIFFERENTIAL EQUATIONS OF THE THIRD ORDER

The paper extends a method for proving algebraic independence from homogeneous third order linear differential equations to nonhomogeneous equations. It applies this extension, together with Shidlovskii’s theorem, to several classes of hypergeometric type E-functions satisfying third order nonhomoge…

THE CAUCHY PROBLEM AND A BOUNDARY-VALUE PROBLEM FOR SECOND-ORDER HYPERBOLIC EQUATIONS DEGENERATING IN THE DOMAIN AND ON ITS BOUNDARY

This paper studies the Cauchy problem and a boundary-value problem for second-order limit hyperbolic equations whose characteristic form is nonnegative and may degenerate arbitrarily inside the domain and on the boundary. Using energy estimates for regularized equations with an added elliptic term a…

Confidence intervals for functions of several unknown parameters

The paper addresses construction of confidence intervals, especially upper confidence bounds, for separable concave functions of many unknown parameters observed through independent Poisson counts. It formulates the general use of confidence sets to obtain interval bounds, then develops three confid…

ON A PROBLEM WITH AN OBLIQUE DERIVATIVE

This paper studies elliptic boundary value problems with an oblique derivative condition in a bounded smooth domain, allowing the oblique vector field to become tangent to the boundary along a smooth submanifold of codimension two. The authors analyze how solvability, regularity, and a priori Sobole…

ON SOME CLASSES OF ORBITS FOR THE GROUP OF UNITRIANGULAR MATRICES

This note studies coadjoint orbits of the group of upper unitriangular matrices, motivated by their relation to irreducible unitary representations of nilpotent Lie groups. Identifying the dual Lie algebra with lower triangular matrices, the paper reduces orbit classification to the consistency of e…

HYPERELLIPTIC CURVES

This note studies the least prime quadratic residue modulo a prime and related distribution questions for ideals in quadratic fields. Combining Burgess’s estimates for character sums, derived from Weil’s results on curves over finite fields, with Siegel’s theorem on quadratic fields, the authors pro…