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24 results on '"Dimovski, Ivan H."'

1. Nonlocal Operational Calculi for Dunkl Operators

Author

Dimovski, Ivan H. and Hristov, Valentin Z.

Subjects
Mathematics - Classical Analysis and ODEs
Abstract

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.

Published
2009
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9. Многомерни операционни смятания за нелокални гранични задачи за еволюционни уравнения

Author

Dimovski, Ivan H. and Tsankov, Yulian Ts.

Subjects
right-inverse operator, evolution equations, multiplier fractions, Department of Complex Analysis, divisor of zero, uniqueness, nonlocal ВVP, non-classical convolutions, ring of multipliers, multivariate convolution algebra, localization
Abstract

[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.

Published
2011

10. Тримерно конволюционно смятане за нелокални еволюционни гранични задачи

Author

Dimovski, Ivan H. and Tsankov, Yulian T.

Subjects
sinе-indicatrix, associated eigenfunctions, Department of Complex Analysis, Duhamel convolution, multiplier fraction, divisor of zero, three-dimensional convolution algebra, multiplier, non-classical convolutions
Abstract

[Dimovski Ivan H.; Димовски Иван Х.]; [Tsankov Yulian T.; Цанков Юлиан Ц.]

Published
2011

11. Точни решения на нелокални гранични задачи за двумерното уравнение на топлопроводността

Author

Dimovski, Ivan H. and Tsankov, Yulian Ts.

Subjects
Duhamel principle, nonlocal BVP, heat equation, multiplier fractions, Department of Complex Analysis, convolution, multiplier, weak solution, integral constraint, convolution algebra
Abstract

[Dimovski Ivan H.; Димовски Иван Х.]; [Tsankov Yulian Ts.; Цанков Юлиан Ц.]

Published
2011

12. Commutants of the Dunkl Operators in C(R)

Author

Dimovski, Ivan H., Hristov, Valentin Z., and Sifi, Mohamed

Subjects
Convolutional Algebra, Department of Complex Analysis, Dunkl Operator, 44A35, Invariant Hyperplane, 42A75, 47L10, 47L80, Mean-Periodic Function, 47A16, Commutant, Multiplier, Cyclic Element
Abstract

* Supported by the Tunisian Research Foundation under 04/UR/15-02., The Dunkl operators., 2000 Mathematics Subject Classification: 44A35; 42A75; 47A16, 47L10, 47L80

Published
2010

13. Точни решения на задачата на Бицадзе-Самарски и някои обобщения

Author

Dimovski, Ivan H. and Tsankov, Yulian Ts.

Subjects
generalized solution, nonlocal BVP, right-inverse operator, Department of Complex Analysis, non-classical convolution, multiplier fraction, multiplier, extended Duamel principle
Abstract

[Dimovski Ivan H.; Димовски Иван Х.]; [Tsankov Yulian Ts.; Цанков Юлиан Ц.] Mathematics Subject Classification (2000): 44A35, 35L20, 35J05, 35J25.

Published
2010

18. Resonance mean-periodic solutions of Euler differential equations.

Author

Dimovski, Ivan H. and Hristov, Valentin Z.

Subjects
*NUMERICAL solutions to differential equations, *EULER method, *CONTINUOUS functions, *OPERATOR theory, *BOUNDARY value problems, *CAUCHY problem, *TOPOLOGICAL spaces
Abstract

The Euler operator δ = tddt is considered in the space C = C(R+) of the continuous functions on R+ = (0,∞). Nonlocal operational calculi for it are developed and used for solving nonlocal Cauchy boundary value problems for Euler differential equations of the form P(δ)y = f with a polynomial P. A function f∈C(R+) is said to be mean-periodic for the Euler operator with respect to the linear functional [uppercase_phi_synonym] (or simply [uppercase_phi_synonym]-mean-periodic) if [uppercase_phi_synonym]τ{f(tτ)} = 0 identically on R+. The solution of Euler differential equations in mean-periodic functions for δ with respect to an arbitrary linear functional [uppercase_phi_synonym] reduces to non-local homogeneous Cauchy problems. Denoting the algebraic equivalent of the Euler differential operator δ by S, the solution of an Euler differential equation P(δ)y = f in [uppercase_phi_synonym]-mean-periodic functions reduces to the interpretation of y = 1P(S)f as a function. This is done both in the non-resonance and in the resonance cases. [ABSTRACT FROM AUTHOR]

Published
2012
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21. Convolutions, Multipliers and Commutants for the Backward Shift Operator

Author

Dimovski, Ivan H. and Mineff, Dimitar M.

Abstract

[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.

Published
1981

22. Convolutions, Multipliers and Commutants Related to Double Complex Dirichlet Expansions

Author

Božinov, Nikolai S. and Dimovski, Ivan H.

Abstract

[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.

Published
1981

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