Avsyankin Oleg Gennadievich

+7(863) 218-40-00 ext. 14018; +7(8634) 68-08-90 ext. 14018;

Звание: Доцент

Degree: Доктор физико-математических наук

Institute of Mathematics, Mechanics, and Computer Science named after of I.I. Vorovich - Head of the department

Southern Federal University - Senior researcher

E-mail:

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Personal page:

https://sfedu.ru/s7/person/ru/ogavsyankin

Personal page in english:

https://sfedu.ru/s7/person/en/ogavsyankin

Research interests:

Multidimensional integral operators with homogeneous and bihomogeneous kernels, convolution type operators, Banach algebras, projection methods for solving operator equations, spectral operator theory, integral operators with periodic kernels, Morrey space

Research projects:

The complete investigation of multidimensional integral operators, whose kernels are homogeneous of degree (-n) and invariant under rotation group, is carried out. In the framework of this investigation we also describe the Banach algebras, generated by such operators, and obtain the criteria of the applicability of projection methods to operators with homogeneous kernels. The C*-algebra generated by multidimensional integral operators with bihomogeneous kernels is investigated. For operators with bihomogeneous kernel the criterion of the applicability of the projection method is obtained. Necessary and sufficient conditions for invertibility and Noethericity for integral operators with homogeneous-difference kernels are obtained.