Sonine Transform Associated to the Dunkl Kernel on the Real Line
We consider the Dunkl intertwining operator Vα and its dual tVα, we define and study the Dunkl Sonine operator and its dual on R. Next, we introduce complex powers of the Dunkl Laplacian Δα and establish inversion formulas for the Dunkl Sonine operator Sα,β and its dual tSα,β. Also, we give a Planch...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2008 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2008
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147997 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Sonine Transform Associated to the Dunkl Kernel on the Real Line / F. Soltani // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 20 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862670478061076480 |
|---|---|
| author | Soltani, F. |
| author_facet | Soltani, F. |
| citation_txt | Sonine Transform Associated to the Dunkl Kernel on the Real Line / F. Soltani // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider the Dunkl intertwining operator Vα and its dual tVα, we define and study the Dunkl Sonine operator and its dual on R. Next, we introduce complex powers of the Dunkl Laplacian Δα and establish inversion formulas for the Dunkl Sonine operator Sα,β and its dual tSα,β. Also, we give a Plancherel formula for the operator tSα,β.
|
| first_indexed | 2025-12-07T15:31:32Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147997 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:31:32Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Soltani, F. 2019-02-16T16:21:36Z 2019-02-16T16:21:36Z 2008 Sonine Transform Associated to the Dunkl Kernel on the Real Line / F. Soltani // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 20 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 43A62; 43A15; 43A32 https://nasplib.isofts.kiev.ua/handle/123456789/147997 We consider the Dunkl intertwining operator Vα and its dual tVα, we define and study the Dunkl Sonine operator and its dual on R. Next, we introduce complex powers of the Dunkl Laplacian Δα and establish inversion formulas for the Dunkl Sonine operator Sα,β and its dual tSα,β. Also, we give a Plancherel formula for the operator tSα,β. This paper is a contribution to the Special Issue on Dunkl Operators and Related Topics. The author is very grateful to the referees and editors for many critical comments on this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Sonine Transform Associated to the Dunkl Kernel on the Real Line Article published earlier |
| spellingShingle | Sonine Transform Associated to the Dunkl Kernel on the Real Line Soltani, F. |
| title | Sonine Transform Associated to the Dunkl Kernel on the Real Line |
| title_full | Sonine Transform Associated to the Dunkl Kernel on the Real Line |
| title_fullStr | Sonine Transform Associated to the Dunkl Kernel on the Real Line |
| title_full_unstemmed | Sonine Transform Associated to the Dunkl Kernel on the Real Line |
| title_short | Sonine Transform Associated to the Dunkl Kernel on the Real Line |
| title_sort | sonine transform associated to the dunkl kernel on the real line |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147997 |
| work_keys_str_mv | AT soltanif soninetransformassociatedtothedunklkernelontherealline |