Dunkl-Sobolev spaces of exponential type and applications. Issue 1 (2011)

• Record Type: Journal Article
• Authors: Mejjaoli Mejjaoli, Hatem Hatem
• Other Names: Birnir Birnir Björn Björn Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 9:Issue 1(2011)
• Page Start: 41
• Page End: 66
• Publication Date: 2011
• Subjects: Dunkl operators; Dunkl-Sobolev spaces of exponential type; Pseudo differential-difference operator; Reproducing kernel; Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2011/728563
• Languages: English
• ISSNs: 0972-6802

Abstract

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.