2019
Том 71
№ 7

# Kalyuzhnyi A. A.

Articles: 10
Article (Russian)

### Finding cocycles in the bicrossed product construction for Lie groups

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

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

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

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

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

Article (Ukrainian)

### Hypercomplex systems originating from orthogonal polynomials

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

Article (Ukrainian)

### Representations of hypercomplex systems with locally compact basis

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

Article (Ukrainian)

### Existence theorem for multiplicative measures

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

Article (Ukrainian)

### Nuclear function spaces on the base of a hypercomplex system

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

Article (Ukrainian)

### Integral representation of exponentially convex functions

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