2019
Том 71
№ 11

All Issues

Kalenyuk P. I.

Articles: 3
Article (Ukrainian)

Spectral properties of nonself-adjoint nonlocal boundary-value problems for the operator of differentiation of even order

Baranetskij Ya. O., Kalenyuk P. I., Kolyasa L. I.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 6. - pp. 739-751

We study spectral properties of an essentially nonself-adjoint problem generated by nonlocal multipoint conditions for the operator of differentiation of order 2n and analyze the cases of regular and irregular Birkhoff boundary conditions. A system of root functions of the problem and elements of biorthogonal systems are constructed. We also establish sufficient conditions under which these systems are complete and form a Riesz basis under certain additional assumptions.

Article (Ukrainian)

Method for separation of variables for bilinear matrix functional equation and its applications

Kalenyuk P. I., Nytrebych Z. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1201–1209

Necessary and sufficient conditions for the solvability of a bilinear matrix functional equation are presented. The conditions are applied in the construction of the solutions of systems of partial differential equations.

Article (Russian)

A generalization of the method of separation of variables

Kalenyuk P. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1974. - 26, № 5. - pp. 652–657