2019
Том 71
№ 6

All Issues

Ostrovskii V. L.

Articles: 7
Article (Ukrainian)

On spectral theorems for families of linearly connected self-adjoint operators with given spectra associated with extended Dynkin graphs

Ostrovskii V. L., Samoilenko Yu. S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 11. - pp. 1556–1570

We prove spectral theorems for families of linearly connected self-adjoint operators with given special spectra associated with extended Dynkin graphs. We establish that all irreducible families of linearly connected operators with arbitrary spectra associated with extended Dynkin graphs are finite-dimensional.

Article (Ukrainian)

Representation of an algebra associated with the Dynkin graph $\tilde E_7$

Ostrovskii V. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 9. - pp. 1193–1202

We describe the structure of pairs of self-adjoint operators $A$ and $B$ whose spectra belong to the set $\{±1/2, ±3/2\}$ and for which $(A+B)^2 = I$. Such pairs of operators determine a representation of a *-algebra $A_{\tilde E_7 }$ associated with the extended Dynkin graph $\tilde E_7$.

Article (Russian)

Representations of *-algebras and many-dimensional dynamical systems

Ostrovskii V. L., Turovskaya L. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1995. - 47, № 4. - pp. 488–497

The procedure developed earlier for investigation of representations of *-algebras is generalized to a wider class of operator relations. In particular, the developed technique is used for description of all irreducible representations of a nonstandard three-dimensional quantum sphere.

Article (Ukrainian)

An application of the projective spectral theorem to commuting families of operators

Ostrovskii V. L., Samoilenko Yu. S.

Full text (.pdf)

Ukr. Mat. Zh. - 1988. - 40, № 4. - pp. 469-481

Article (Ukrainian)

Expansion in eigenfunctions of families of commuting operators and representations of commutation relations

Berezansky Yu. M., Ostrovskii V. L., Samoilenko Yu. S.

Full text (.pdf)

Ukr. Mat. Zh. - 1988. - 40, № 1. - pp. 106-109

Article (Ukrainian)

Construction of quasiinvariant measures on a class of groups that are not locally compact

Ostrovskii V. L.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 4. - pp. 524–526

Article (Ukrainian)

Irreducible representations of the group of infinite upper triangular matrices

Ostrovskii V. L.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 2. - pp. 255–259