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Journal of Function Spaces and Applications
Volume 9 (2011), Issue 1, Pages 41-66
http://dx.doi.org/10.1155/2011/728563

Dunkl-Sobolev spaces of exponential type and applications

Department of Mathematics, Faculty of sciences of Tunis, Campus 1060.Tunis, Tunisia

Received 1 July 2008

Academic Editor: Björn Birnir

Copyright © 2011 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the Sobolev spaces of exponential type associated with the Dunkl operators. Some properties including completeness and imbedding theorem are proved. Next we introduce a classes of symbols of exponential type and the associated pseudo-differential-difference operators, which naturally act on the Dunkl-Sobolev spaces of exponential type. Finally using the theory of reproducing kernels some applications are given for these spaces.