Dunkl-Sobolev spaces of exponential typeand applications

摘要

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.