2019
Том 71
№ 8

All Issues

Brief Communications (Ukrainian)

Mark Grigor'evich Krein

Berezansky Yu. M.

Ukr. Mat. Zh. - 1994νmber=6. - 46, № 3. - pp. 

Article (Ukrainian)

Unitary colligations and parametrization formulas

↓ Abstract

Ukr. Mat. Zh. - 1994νmber=6. - 46, № 3. - pp. 147–154

The aim of this paper is to describe, in a rather concise but relatively self-contained manner, some relations between unitary colligations which are regarded as linear systems, and parametrization formulas for the solutions of some interpolation problems.

Article (Ukrainian)

Spectral theory of a string

Kats I. S.

↓ Abstract

Ukr. Mat. Zh. - 1994νmber=6. - 46, № 3. - pp. 155–176

In this survey, we present the principal results of Krein's spectral theory of a string and describe its development by other authors.

Article (Russian)

Spectral approach to white noise analysis

Berezansky Yu. M., Livinskii V. O., Lytvynov E. V.

↓ Abstract

Ukr. Mat. Zh. - 1994νmber=6. - 46, № 3. - pp. 177–197

By using the spectral projection theorem, we construct the classical Segal transformation as a Fourier transformation in the generalized joint eigenvectors of a certain family of field operators. It is noted that the spectral approach to the Segal transformation, which forms the basis of the analysis of Gaussian white noise, enables one to construct a significant generalization of this transformation.

Article (Ukrainian)

On M. G. Krein's works in the theory of representations and harmonic analysis on topological groups

Vainerman L. I.

↓ Abstract

Ukr. Mat. Zh. - 1994νmber=6. - 46, № 3. - pp. 198–211

This is a brief survey of M. G. Krein's papers in the theory of representations and harmonic analysis on topological groups. These papers are known to be classical and form the basis of numerous contemporary researches into these fields.

Article (Ukrainian)

Uniqueness theorems for rational, algebraic, and algebroid functions

Gol'dberg A. A., P'yana V. A.

↓ Abstract

Ukr. Mat. Zh. - 1994νmber=6. - 46, № 3. - pp. 212–226

A number of pointsA, for which one must define the sets of simpleA-points to determine a rational function, a polynomial, and an algebraic or algebroid function uniquely, is obtained.

Article (Ukrainian)

A class of admissible functions in the principle of invariance of wave operators

Konstantinov A. Yu.

↓ Abstract

Ukr. Mat. Zh. - 1994νmber=6. - 46, № 3. - pp. 227–229

A class of admissible functions that satisfies the well-known invariance principle in the scattering theory is extended.

Article (Ukrainian)

A relation between two results about entire functions of exponential type

Koosis P.

Ukr. Mat. Zh. - 1994νmber=6. - 46, № 3. - pp. 230–243

Article (Ukrainian)

Estimation of the solutions of the Sturm-Liouville equation

Levin B. Ya., Mirochnik L. Ya.

Ukr. Mat. Zh. - 1994νmber=6. - 46, № 3. - pp. 244–278

Article (Ukrainian)

Uniqueness of solutions of boundary-value problems for operator-differential equations on a finite segment and on a semiaxis

Radzievskii G. V.

Ukr. Mat. Zh. - 1994νmber=6. - 46, № 3. - pp. 279–292

Article (Ukrainian)

Factorization of operators. Theory and applications

Sakhnovich L. A.

↓ Abstract

Ukr. Mat. Zh. - 1994νmber=6. - 46, № 3. - pp. 293–304

A survey of the development of Krein's factorization method and its applications is given.