2019
Том 71
№ 11

# Ostrovskii V. L.

Articles: 8
Article (Ukrainian)

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

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 $\tilde E_7$

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

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 (Russian)

### On pairs of unbounded self-adjoint operators satisfying an algebraic relation

Ukr. Mat. Zh. - 1993. - 45, № 9. - pp. 1253–1258

Unbounded pairs of self-adjoint operators A andB satisfying the algebraic relation F 1(A)B=BF 2(A) are studied. For these relations, various definitions of “integrable” pairs of operators are presented and the class of “tame” relations is indicated; for the “tame” relations, the irreducible pairs are described and a structure theorem is presented.

Article (Ukrainian)

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

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

Article (Ukrainian)

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

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

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

Article (Ukrainian)

### Irreducible representations of the group of infinite upper triangular matrices

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