The Range of the Spectral Projection Associated with the Dunkl Laplacian
For s∈ℝ, denote by Pksf the “projection” of a function f in Dℝd into the eigenspaces of the Dunkl Laplacian Δk corresponding to the eigenvalue −s2. The parameter k comes from Dunkl’s theory of differential-difference operators. We shall characterize the range of Pks on the space of functions f∈Dℝd s...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/7803719 |
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| _version_ | 1832556801664483328 |
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| author | Salem Ben Said Hatem Mejjaoli |
| author_facet | Salem Ben Said Hatem Mejjaoli |
| author_sort | Salem Ben Said |
| collection | DOAJ |
| description | For s∈ℝ, denote by Pksf the “projection” of a function f in Dℝd into the eigenspaces of the Dunkl Laplacian Δk corresponding to the eigenvalue −s2. The parameter k comes from Dunkl’s theory of differential-difference operators. We shall characterize the range of Pks on the space of functions f∈Dℝd supported inside the closed ball BO,R¯. As an application, we provide a spectral version of the Paley-Wiener theorem for the Dunkl transform. |
| format | Article |
| id | doaj-art-2c4598b5ed1b4271b476eee64c3b0b52 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-2c4598b5ed1b4271b476eee64c3b0b522025-02-03T05:44:21ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/78037197803719The Range of the Spectral Projection Associated with the Dunkl LaplacianSalem Ben Said0Hatem Mejjaoli1Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain Abu Dhabi, UAEDepartment of Mathematics, College of Science, Taibah University, Al Madinah AL Munawarah, Saudi ArabiaFor s∈ℝ, denote by Pksf the “projection” of a function f in Dℝd into the eigenspaces of the Dunkl Laplacian Δk corresponding to the eigenvalue −s2. The parameter k comes from Dunkl’s theory of differential-difference operators. We shall characterize the range of Pks on the space of functions f∈Dℝd supported inside the closed ball BO,R¯. As an application, we provide a spectral version of the Paley-Wiener theorem for the Dunkl transform.http://dx.doi.org/10.1155/2020/7803719 |
| spellingShingle | Salem Ben Said Hatem Mejjaoli The Range of the Spectral Projection Associated with the Dunkl Laplacian Journal of Function Spaces |
| title | The Range of the Spectral Projection Associated with the Dunkl Laplacian |
| title_full | The Range of the Spectral Projection Associated with the Dunkl Laplacian |
| title_fullStr | The Range of the Spectral Projection Associated with the Dunkl Laplacian |
| title_full_unstemmed | The Range of the Spectral Projection Associated with the Dunkl Laplacian |
| title_short | The Range of the Spectral Projection Associated with the Dunkl Laplacian |
| title_sort | range of the spectral projection associated with the dunkl laplacian |
| url | http://dx.doi.org/10.1155/2020/7803719 |
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