Table of Contents
Journal of Operators
Volume 2014, Article ID 659069, 9 pages
http://dx.doi.org/10.1155/2014/659069
Research Article

Uncertainty Principles and Extremal Functions for the Dunkl -Multiplier Operators

Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 114, Jazan, Saudi Arabia

Received 19 November 2013; Accepted 12 June 2014; Published 17 August 2014

Academic Editor: Aref Jeribi

Copyright © 2014 Fethi Soltani. 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 some class of Dunkl -multiplier operators; and related to these operators we establish the Heisenberg-Pauli-Weyl uncertainty principle and Donoho-Stark’s uncertainty principle. We give also an application of the theory of reproducing kernels to the Tikhonov regularization on the Sobolev-Dunkl spaces.