Nonlocal Operational Calculi for Dunkl Operators
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 operationa...
Збережено в:
| Дата: | 2009 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149174 |
| Теги: |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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. |
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