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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2009 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2009
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149174 |
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| Zitieren: | 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. |
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Dimovski, I.H. Hristov, V.Z. 2019-02-19T18:12:26Z 2019-02-19T18:12:26Z 2009 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. 1815-0659 2000 Mathematics Subject Classification: 44A40; 44A35; 34K06 https://nasplib.isofts.kiev.ua/handle/123456789/149174 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Nonlocal Operational Calculi for Dunkl Operators Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Nonlocal Operational Calculi for Dunkl Operators |
| spellingShingle |
Nonlocal Operational Calculi for Dunkl Operators Dimovski, I.H. Hristov, V.Z. |
| title_short |
Nonlocal Operational Calculi for Dunkl Operators |
| title_full |
Nonlocal Operational Calculi for Dunkl Operators |
| title_fullStr |
Nonlocal Operational Calculi for Dunkl Operators |
| title_full_unstemmed |
Nonlocal Operational Calculi for Dunkl Operators |
| title_sort |
nonlocal operational calculi for dunkl operators |
| author |
Dimovski, I.H. Hristov, V.Z. |
| author_facet |
Dimovski, I.H. Hristov, V.Z. |
| publishDate |
2009 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149174 |
| citation_txt |
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. |
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2025-12-01T23:50:02Z |
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2025-12-01T23:50:02Z |
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1850861202773639168 |