Table of contents

In my paper On linear widths of Sobolev classes and chains of extremal subspaces (Mat. Sb. 113 (155) (1980), no. 3, 437-463 = Math. USSR Sb. 41 (1982), no. 3, 361-382) the following corrections must be made. All restrictions on (, ) in Theorem 2.3 and also in the relations (2.29) and (2.31) must be replaced by the stronger restriction . As B. S. Kashin has shown (Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1981, no. 5, 50-54), when the asymptotics for -widths indicated in our paper is violated. In addition, there is a misprint just before the relation (2.31): in place of read . The other restrictions on and are correct. The cited errors occur in the statement of theorems that follow from the main results of the paper; they do not affect the main results.

Let be the space of infinitely differentiable functions on the unit circle . The operator of multiplication by the independent variable acts in this space: . This article deals with a description of the invariant subspaces of the operator . Bibliography: 11 titles.

For functions , , nondecreasing, and a positive operator in a Banach space, the operators and are constructed, their products and superpositions are investigated and the moment inequality as well as other estimates are proved. The results are generalized to the case when does not exist or is not bounded. Bibliography: 21 titles.

The question of boundary values for solutions of elliptic equations in domains with Lyapunov boundary is investigated. Bibliography: 7 titles.

A sequence of new knot invariants is constructed by using the relationship between the theory of distributive groupoids and knot theory. Bibliography: 3 titles.

The main result in the article is Theorem.Let be a closed set such that and is a pseudoconvex domain. If for almost every complex line passing through 0 the intersection is polar in , then is a pluripolar set in . This theorem is then applied to the analysis of sets of singularities of holomorphic functions which are rapidly approximated by rational functions. Bibliography: 21 titles.

This paper is concerned with free groups of certain varieties. Bibliography: 12 titles.

This paper contains a number of results on the logarithmic asymptotics and the asymptotic distribution of zeros of polynomials that are orthonormal on the real axis or semiaxis with respect to weight functions of the type . Bibliography: 10 titles.

In this paper the author considers the problem of the existence and uniqueness of a surface with given extrinsic curvature in three-dimensional Galilean space. A new approach to the definition of the extrinsic curvature of a convex surface is given. Bibliography: 15 titles.

The first Green's formula for integrals on a Hilbert space is proved. Using this formula the authors establish, in particular, the following result. Theorem.A nondegenerate quadratic functional of a Wiener random process has an infinitely differentiate distribution function. Bibliography: 9 titles.

In this paper we study singularities of convex hulls of smooth submanifolds of an affine space whose codimension is not greater than two. We prove that in spaces of dimension five or higher some of these singularities have functional moduli with respect to the group of diffeomorphisms of the ambient space that cannot be removed by small deformations of the manifold. Bibliography: 2 titles.

The author studies the imbedding of the Hecke -ring of the modular group of genus in the Hecke ring of the group given by

It is proved that the Hecke polynomial of splits over , and the coefficients of the factors can be written explicitly in terms of the coefficients of the Hecke polynomial of genus and "negative" powers of a particular element of . The " power" of is computed and a formula for is presented. The results that are obtained permit one to describe a large class of power series constructed from the Fourier-Jacobi coefficients by means of eigenfunctions with denominators depending only on the eigenvalues. Bibliography: 19 titles.

The author constructs examples of orthonormal systems giving an answer to some questions in the theory of orthogonal series. Bibliography: 15 titles.