2019
Том 71
№ 9

All Issues

Anniversaries (Russian)

Mark Grigor'evich Krein

Mitropolskiy Yu. A.

Ukr. Mat. Zh. - 1994νmber=3. - 46, № 1-2. - pp. 3–4

Article (Russian)

On M. G. Krein's papers in the theory of spaces with an indefinite metric

Azizov T. Ya., Ginsburg Yu. P., Langer H.

↓ Abstract

Ukr. Mat. Zh. - 1994νmber=3. - 46, № 1-2. - pp. 5–17

This is a surv ey of the papers by M. G. Krein (and his disciples) devoted to the theory of operators in the spaces with indefinite metric and its applications.

Article (English)

On time dependent orthogonal polynomials on the unit circle

Ben-Artzi A., Gohberg I. C.

↓ Abstract

Ukr. Mat. Zh. - 1994νmber=3. - 46, № 1-2. - pp. 18–36

Two index formulas for operators defined by infinite band matrices are proved. These results may be interpreted as a generalization of the classical theorem of M. G. Krein for orthogonal polynomials. The proofs are based on dichotomy and nonstationary inertia theory.

Article (English)

New aspects of Krein's extension theory

Brasche J. F., Koshmanenko V. D., Neidhardt H.

↓ Abstract

Ukr. Mat. Zh. - 1994νmber=3. - 46, № 1-2. - pp. 37–54

The extension problem for closed symmetric operators with a gap is studied. A new kind of parametrization of extensions (the so-called Krein model) is developed. The notion of a singular operator plays the key role in our approach. We give the explicit description of extensions and establish the spectral properties of extended operators.

Article (Ukrainian)

Theory of self-adjoint extensions of symmetric operators. entire operators and boundary-value problems

Gorbachuk M. L., Gorbachuk V. I.

↓ Abstract

Ukr. Mat. Zh. - 1994νmber=3. - 46, № 1-2. - pp. 55–62

This is a brief survey of M. G. Krein's contribution to the theory of self-adjoint extensions of Hermitian operators and to the theory of boundary value problems for differential equations. The further development of these results is also considered.

Article (Ukrainian)

On M. G. Krein's contribution to the moment problem

Nudel'man A. A.

↓ Abstract

Ukr. Mat. Zh. - 1994νmber=3. - 46, № 1-2. - pp. 63–75

This is a survey of М. G. Krein's papers devoted to the moment problem.

Article (Russian)

M. G. Krein's ideas in the theory of orthogonal polynomials

Osilenker B. P.

↓ Abstract

Ukr. Mat. Zh. - 1994νmber=3. - 46, № 1-2. - pp. 76–86

We present a survey of M. G. Krein's ideas in tho theory of orthogonal polynomials.

Article (Russian)

M. G. Krein's investigations in the theory of entire and meromorphic functions and their further development

Ostrovskii I. V.

↓ Abstract

Ukr. Mat. Zh. - 1994νmber=3. - 46, № 1-2. - pp. 87–99

This is a survey of М. G. Krein's results in the theory of entire and meromorphic functions. Their further development is also discussed.

Article (Russian)

Szego-Kolmogorov-Krein theorems on weighted trigonometrical approximation and Carleman-type relations

Bart V. A., Khavin V. P.

↓ Abstract

Ukr. Mat. Zh. - 1994νmber=3. - 46, № 1-2. - pp. 100–127

In view of the well-known Szego - Kolmogorov - Krein theorems on weighted approximation by the functions with semibounded spectrum (on a circle or a line), an efficient construction is suggested, which enables one to realize these approximations. It is based on relations similar to the Carleman tor-mula reconstructing an analytic function in terms its trace on the boundary of the domain of definition.

Article (Russian)

On M. G. Krein's work in the theory of linear periodic Hamiltonian systems

Yakubovich V. A.

↓ Abstract

Ukr. Mat. Zh. - 1994νmber=3. - 46, № 1-2. - pp. 128–144

We present the basic ideas of the theory of linear periodic Hamiltonian systems.