2019
Том 71
№ 10

All Issues

Kalyuzhnyi A. A.

Articles: 10
Article (Russian)

Finding cocycles in the bicrossed product construction for Lie groups

Chapovsky Yu., Kalyuzhnyi A. A., Podkolzin G. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 11. - pp. 1510–1522

We find an explicit formula for finding pairs of cocycles for the construction of examples of locally compact quantum groups by using the bicrossed product of Lie groups.

Article (Russian)

Conditional Expectations on Compact Quantum Groups and Quantum Double Cosets

Chapovsky Yu., Kalyuzhnyi A. A., Podkolzin G. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 5. - pp. 644–653

We prove that a conditional expectation on a compact quantum group that satisfies certain conditions can be decomposed into a composition of two conditional expectations one of which is associated with quantum double cosets and the other preserves the counit.

Article (English)

Factorization of Conditional Expectations on Kac Algebras and Quantum Double Coset Hypergroups

Chapovsky Yu., Kalyuzhnyi A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 12. - pp. 1669-1677

We prove that a conditional expectation on a Kac algebra, under certain conditions, decomposes into a composition of two conditional expectations of a special type and gives rise to a compact quantum hypergroup connected to a quantum Gelfand pair.

Article (Russian)

On Orthogonal Appell-Like Polynomials in Non-Gaussian Analysis

Kachanovskii N. A., Kalyuzhnyi A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 7. - pp. 892-907

We study an example of the construction of a non-Gaussian analysis using orthogonal generalized Appell-like polynomials with the generating function $$\frac{1}{{\sqrt {1 - 2a{\lambda + \lambda }^{2}} } }\cos \left( {\sqrt x \frac{1}{2}\int\limits_{0}^{\lambda } {\frac{{du}}{{\sqrt {u - 2au^2 + u^3 } }}} } \right),\quad a >1,$$ in the model one-dimensional case. The main results are a detailed intrinsic description of spaces of test functions, a description of generalized translation operators, and the investigation of integral C- and S-transformations.

Article (Ukrainian)

Spectral theory of orthogonal polynomials of several variables

Gekhtman M. I., Kalyuzhnyi A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 10. - pp. 1437–1440

Article (Ukrainian)

Hypercomplex systems originating from orthogonal polynomials

Berezansky Yu. M., Kalyuzhnyi A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 3. - pp. 275–284

Article (Ukrainian)

Representations of hypercomplex systems with locally compact basis

Berezansky Yu. M., Kalyuzhnyi A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1984. - 36, № 4. - pp. 417 - 421

Article (Ukrainian)

Existence theorem for multiplicative measures

Kalyuzhnyi A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1983. - 35, № 3. - pp. 369 — 371

Article (Ukrainian)

Nuclear function spaces on the base of a hypercomplex system

Berezansky Yu. M., Kalyuzhnyi A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1983. - 35, № 1. - pp. 9—17

Article (Ukrainian)

Integral representation of exponentially convex functions

Kalyuzhnyi A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1982. - 34, № 3. - pp. 370—373