Выступление с докладом на международном семинаре
10.09.2020
Название доклада: Convolution operators via orthogonal polynomials.
Аннотация
The foundation of models describing various physical-chemical processes can be obtained by virtue of fractional calculus methods, the central point of which is a concept of the Riemann-Liouville operator acting in weighted Lebesgue spaces. In its own turn, the operator theory methods play an important role in applications and need not any of special advertising. Having forced by these reasons, we deal with mapping theorems for operators acting on Banach spaces in order to obtain afterwards the desired results applicable to integral operators.
In this paper we offer one method of studying the Sonin operator ( Sonine N. Sur la generalization d'une formulae d'Abel, Acta Math., (4), 171—176, 1884). We claim the existence and uniqueness theorem (criterion) formulated in terms of the Jacoby series coefficients which gives us an opportunity to find and classify a solution of the Sonin-Abel equation due to an asymptotic of the right-hand side.
Аннотация
The foundation of models describing various physical-chemical processes can be obtained by virtue of fractional calculus methods, the central point of which is a concept of the Riemann-Liouville operator acting in weighted Lebesgue spaces. In its own turn, the operator theory methods play an important role in applications and need not any of special advertising. Having forced by these reasons, we deal with mapping theorems for operators acting on Banach spaces in order to obtain afterwards the desired results applicable to integral operators.
In this paper we offer one method of studying the Sonin operator ( Sonine N. Sur la generalization d'une formulae d'Abel, Acta Math., (4), 171—176, 1884). We claim the existence and uniqueness theorem (criterion) formulated in terms of the Jacoby series coefficients which gives us an opportunity to find and classify a solution of the Sonin-Abel equation due to an asymptotic of the right-hand side.
