Dunkl multiplier operators and applications

Abstract

We study some class of Dunkl multiplier operators; and we establish for them some versions of uncertainty principles. For these operators we give also an application of the theory of reproducing kernels to the Tikhonov regularization on the Sobolev–Dunkl spaces.

Keywords:

• Sobolev–Dunkl spaces
• Dunkl multiplier operators
• uncertainty principles
• Tikhonov regularization
• extremal functions

2010 Mathematics Subject Classification:

• 42B10
• 42B15
• 46E35

Acknowledgements

The author is very grateful to the referee for many critical comments on this work.

Funding

The author thanks the Deanship of Scientific Research-Jazan University for its support in financing this research project.