2017
Том 69
№ 9

All Issues

Volume 46, № 3, 1994

Brief Communications (Ukrainian)

Mark Grigor'evich Krein

Berezansky Yu. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 3. - pp. 

Article (Ukrainian)

Unitary colligations and parametrization formulas

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 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   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 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   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 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   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 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   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 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   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 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.

Full text (.pdf)

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

Article (Ukrainian)

Estimation of the solutions of the Sturm-Liouville equation

Levin B. Ya., Mirochnik L. Ya.

Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 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.

Full text (.pdf)

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

Article (Ukrainian)

Factorization of operators. Theory and applications

Sakhnovich L. A.

↓ Abstract   |   Full text (.pdf)

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

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