2018
Том 70
№ 9

All Issues

Livinskii V. O.

Articles: 4
Article (Ukrainian)

Essential normality of some classes of operators in infinite tensor products of Hilbert spaces

Livinskii V. O.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 9. - pp. 1164–1170

The essential normality of some classes of operators in stabilized infinite tensor products of Hilbert spaces is established by using the general criteria for the domains of definition of spectral integrals to be essential.

Article (Ukrainian)

Essential normality of some classes of operators in tensor products of Hilbert spaces

Livinskii V. O.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 7. - pp. 878–885

We establish general criteria for the domains of definition of spectral integrals to be essential. On the basis of these criteria, we prove that some classes of operators are essentially normal in tensor products of Hilbert spaces.

Article (Ukrainian)

A remark about orthogonal polynomials

Livinskii V. O.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 4. - pp. 389–392

We suggest a renewal method for reconstructing a density in a special case by a system of polynomials orthogonal with respect to it.

Article (Russian)

Spectral approach to white noise analysis

Berezansky Yu. M., Livinskii V. O., Lytvynov E. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 3. - pp. 177–197

By using the spectral projection theorem, we construct the classical Segal transformation as a Fourier transformation in the generalized joint eigenvectors of a certain family of field operators. It is noted that the spectral approach to the Segal transformation, which forms the basis of the analysis of Gaussian white noise, enables one to construct a significant generalization of this transformation.