Nonlocal Operational Calculi for Dunkl Operators

The one-dimensional Dunkl operator $D_k$ with a non-negative parameter $k$, is considered under an arbitrary nonlocal boundary value condition. The right inverse operator of $D_k$, satisfying this condition is studied. An operational calculus of Mikusinski type is developed. In the frames of this operational calculi an extension of the Heaviside algorithm for solution of nonlocal Cauchy boundary value problems for Dunkl functional-differential equations $P(D_k)u=f$ with a given polynomial $P$ is proposed. The solution of these equations in mean-periodic functions reduces to such problems. Necessary and sufficient condition for existence of unique solution in mean-periodic functions is found

The Finite Leontiev Transform: Operational Properties and Multipliers

[Dimovski Ivan H.; Димовски Иван Х.

Операционен подход към нелокални задачи на Коши

[Dimovski Ivan H.; Димовски Иван Х.]; [Spiridonova Margarita; Спиридонова Маргарита

Convolutions, Multipliers and Commutants Related to Double Complex Dirichlet Expansions

[Božinov Nikolai S.; Bozhinov N. S.; Божинов Николай С.]; [Dimovski Ivan H.; Димовски Иван Х.]An algebraic approach to the problem of expanding of functions of several complex variables in multiple Dirichlet series in polydomains is proposed. An explicit representation of the coefficient convolutions and multipliers of Gromov-Leontiev’s expansion is found. By the way, the commutant of the operators for partial differentiation in certain invariant subspaces is determined

Комутанти на оператора на Ойлер и съответни средно-периодични функции

[Dimovski Ivan H.; Dimovski Ivan Hristov; Димовски Иван Христов]; [Hristov Valentin Z.; Hristov Valentin Zdravkov; Христов Валентин Здравков

Многомерни операционни смятания за нелокални гранични задачи за еволюционни уравнения

[Dimovski Ivan H.; Димовски Иван Х.]; [Tsankov Yulian Ts.; Цанков Юлиан Ц.]Here we propose a direct operational calculus approach to nonlocal boundary value problems for a large class of linear evolution equations with several space variables and one time variable. PACS: 44A35, 44A45, 35K20, 35K15, 35J25

Complex Inversion Formulas for the Obrechkoff Transform

[Dimovski Ivan H.; Димовски Иван Х.]; [Kiryakova Virginia S.; Кирякова Виржиния С.

Convolutions, Multipliers and Commutants for the Backward Shift Operator

[Dimovski Ivan H.; Димовски Иван Х.]; [Mineff Dimitar M.; Minev Dimitar; Минев Димитър М.]An algebraic approach to the backward shift operator U* is developed. The convolutions of all linear right inverse operators of U* are found. The multiplier operators of these convolutions are determined. An explicit representation of the commutant of U* in an invariant hyperplane is given. An application to the multiplier problem of T. A. Leontieva's expansions in a closed domain is made

Commutants of the Pommiez operator

The Pommiez operator (Δf)(z)=(f(z)−f(0))/z is considered in the space ℋ(G) of the holomorphic functions in an arbitrary finite Runge domain G. A new proof of a representation formula of Linchuk of the commutant of Δ in ℋ(G) is given. The main result is a representation formula of the commutant of the Pommiez operator in an arbitrary invariant hyperplane of ℋ(G). It uses an explicit convolution product for an arbitrary right inverse operator of Δ or of a perturbation Δ−λI of it. A relation between these two types of commutants is found