Table of contents

Necessary and sufficient conditions are established under which a solution of an elliptic equation in a ball has a limit in the mean on the boundary sphere. Bibliography: 3 titles.

In this paper the classes of functions are studied, and the topological spaces are constructed from them. In particular, a necessary and sufficient condition guaranteeing a countable base in is found. Classes of functions conjugate (relative to sum) to are introduced and investigated. Bibliography: 7 titles.

We study the problem of completeness of the system of eigenvectors and associated vectors of operator-valued functions which are analytic in an angular region and which assume values in the ring of bounded linear operators in a separable Hilbert space . As a corollary of the fundamental theorem proved in this paper we obtain the following result. Theorem 1. Let , where, andis a completely continuous positive operator; moreover, letfor some. Then for every the closed linear hull of the eigenvectors and associated vectors of (or) which correspond to the eigenvalues lying in the angular region has finite defect in. Bibliography: 20 titles.

We consider curves having either a uniformization by the upper half-plane or a Mumford uniformization by discrete arithmetic subgroups of corresponding to quaternion algebras with center , with a global field of (possibly nonzero) characteristic , being totally real if ; is the completion of with respect to a valuation which is real or non-Archimedean. The principal result is a theorem that in characteristic the curves corresponding to algebras related in a certain sense coincide. Bibliography: 10 titles.

We obtain estimates for the derivative of a power quasipolynomial that are analogous to the well-known inequality of A. A. Markov, estimates for a quasipolynomial in terms of a restriction of it, and certain other inequalities. Bibliography: 2 titles.

In this paper we single out a class of even functional that have an infinite number of critical values that are stable under small perturbations by functional that do not have the property of being even. We give applications to the problem of periodic solutions of a system of ordinary differential equations and to the Dirichlet problem for quasilinear elliptic equations. The basis for the proof of most of the results is made up from the ideas of the method of monotone operators and a variant of the Ljusternik-Šnirel'man theory (cf. [3; MR 45 # 5836]). Bibliography: 12 titles.

In this paper a family of irreducible unitary representations of the group is constructed, where is an open set in , . The group consists of all infinitely differentiable mappings with compact support ( outside some compact set) and is furnished with pointwise multiplication. The author's construction is a modification of the well-known Araki construction. The representations constructed here act in the class of functional on a space dual to a nuclear space and furnished with a Gaussian measure. Bibliography: 7 titles.

Independent systems of defining relations are found for free periodic groups of odd exponent with . Bibliography: 3 titles.

Holomorphic functions having algebraic singular sets of finite order in are characterized by the degree of special rational approximations in a neighborhood of a point of holomorphy. Bibliography: 7 titles.

Let be a Jordan domain with smooth boundary, a function meromorphic in , and the holomorphic component of in . It is shown that , where is the number of poles of in . Bibliography: 8 titles.