2019
Том 71
№ 2

All Issues

Chernobai O. B.

Articles: 5
Article (Ukrainian)

Generalized kernels of the Toeplitz type for exponentially convex functions

Chernobai O. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2016. - 68, № 2. - pp. 278-288

We prove an integral representation for the generalized kernels of the Toeplitz type connected with exponentially convex functions but not with positive-definite functions.

Brief Communications (Ukrainian)

On generalized solutions of differential equations with several operator coefficients

Chernobai O. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 6. - pp. 860-864

The theorem on the smoothness of generalized solutions of differential equations with some operational coefficients is proved.

Brief Communications (Ukrainian)

On generalized solutions of differential equations with operator coefficients

Chernobai O. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 5. - pp. 715–720

We prove a theorem on the smoothness of generalized solutions of differential equations with operator coefficients.

Article (Russian)

Spectral representation for generalized operator-valued Toeplitz kernels

Chernobai O. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 12. - pp. 1698–1710

We prove an integral representation for operator-valued Toeplitz kernels. The proof is based on the spectral theory of the corresponding differential operator constructed from this kernel and acting in a Hilbert space.

Article (Ukrainian)

On the Spectral Theory of Generalized Toeplitz Kernels

Chernobai O. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 6. - pp. 850-857

We give a criterion for the denseness of the Fourier transform in the space L 2 associated with spectral representation of positive-definite Toeplitz kernels.