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Volume 10, Issue 2, Article 55 |
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Generalized Dunkl-Sobolev Spaces of Exponential Type and Applications
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Authors: |
Hatem Mejjaoli, |
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Keywords:
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Dunkl operators, Dunkl-Bessel-Laplace operator, Generalized Dunkl-Sobolev spaces of exponential type, Pseudo differential-difference operators, Reproducing kernels. |
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Date Received:
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22/03/08 |
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Date Accepted:
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23/05/09 |
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Subject Codes: |
Pri: 46F15. Sec: 46F12.
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Editors: |
Sever S. Dragomir, |
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Abstract: |
We study the Sobolev spaces of exponential type associated with the Dunkl-Bessel Laplace operator. Some properties including completeness and the imbedding theorem are proved. We next introduce a class of symbols of exponential type and the associated pseudo-differential-difference operators, which naturally act on the generalized Dunkl-Sobolev spaces of exponential type. Finally, using the theory of reproducing kernels, some applications are given for these spaces.
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