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Nonlocal Operational Calculi for Dunkl Operators
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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Nonlocal Operational Calculi for Dunkl Operators
Інший ID:
2000 Mathematics Subject Classification: 44A40; 44A35; 34K06
Посилання:
Nonlocal Operational Calculi for Dunkl Operators / I.H. Dimovski, V.Z. Hristov // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 16 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Dunkl Operators and Related Topics. The authors are very grateful to the editors and to the referees for the constructive and valuable comments and recommendations.
Дата:
2009
Переглядів:
416
Завантажень:
214
Анотація:
The one-dimensional Dunkl operator Dk with a non-negative parameter k, is considered under an arbitrary nonlocal boundary value condition. The right inverse operator of Dk, 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(Dk)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.
