Chernobai O. B.
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.
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.
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.
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.
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.