Table of contents

It is shown that the m-meromorphic extensions of f(z) = Σ₀^∞f_kz^k can be described in terms of the asymptotic distribution of the poles of the mth row of the Padé table of f(z). Bibliography: 2 titles.

In the article, stability with respect to initial data of a family of explicit nonselfadjoint operator-difference schemes defined on the direct sum of two spaces is studied. Necessary and sufficient conditions for stability in the energy norms are obtained. The equivalence of the norms obtained to the mesh norm L₂ is proved. Bibliography: 3 titles.

In this paper a theory of zeta-functions with Euler product and functional equation is constructed for the case of Hilbert-Siegel functions of a totally real one-class field of algebraic numbers. Bibliography: 14 titles

This paper discusses the application of exact difference schemes to the construction and study of difference schemes for generalized solutions. Bibliography: 15 titles.

This paper studies a multiparameter family of left-invariant metrics on simple Lie groups which generalizes the inertia tensor of an n-dimensional rigid body. A class of solutions is produced for the geodesic equations on simple linear groups expressed in terms of quasipolynomials. For groups of complex matrices with determinant one, explicit formulas are found for the matrix elements of geodesics. The matrix elements are polynomials in exponentials and in theta-functions on Riemann surfaces. Bibliography: 11 titles.

Let , where , , , for , and , in which the function satisfies the radiation conditions

The asymptotics of the scattering amplitude for is obtained as . It can be represented in the form of a sum of two canonical operators of V.P. Maslov, constructed from the -dimensional Lagrangian manifolds , . Let be the -dimensional Lagrangian manifold comprised of the bicharacteristics corresponding to the problem under consideration, and let be a parameter along the bicharacteristics. The manifold can be obtained from by passing to spherical coordinates in projecting on to and letting s go to infinity. The manifold coincides with for . Bibliography: 5 titles

It is proved that there exists an orthonormal system that is not a system of unconditional convergence and, moreover, is not complete in the L₂-metric on any set of positive measure. Bibliography: 8 titles.

A metric ds²admits a Σ-realization if there is a realization of it in E³ in the form of a surface whose boundary lies on a given surface Σ. This paper proves the existence of Σ-realizations of a certain class of metrics of positive curvature for surfaces of quite general form, and describes a number of possible Σ-realizations of the given metric. The proof is based on a consideration of a nonlinear boundary-value problem for immersion equations. Bibliography: 3 titles.

This article contains a study of the matrix groups E_n(R), SL_n,SL'_n, GL_n and GL'_n over an arbitrary commutative ring R, for n ≥ 4. Bibliography: 24 titles.

The author considers a second order elliptic equation in a cylinder (0, d) × G ⊂ Rⁿ with the following boundary conditions: the trace of the solution for x₁ = 0, d is equal to a linear combination of traces for x₁ = d_i (i = 1,...,m; 0 < d_i < d), with the trace on the lateral surface of the cylinder equal to zero. It is proved that the spectrum of the operator under consideration is discrete and semibounded, and also that the operator itself is Fredholm. The results are applied to the study of the spectrum of a particular differential-difference operator. Bibliography: 13 titles.