AN L^p HEISENBERG-PAULI-WEYL UNCERTAINTY PRINCIPLE FOR THE DUNKL TRANSFORM

Abstract

In this paper, we give a generalization of the Heisenberg-PauliWeyl uncertainty inequality for the Dunkl transform on Rdin Lp-norm

Keywords

• Dunkl transform,Heisenberg-Pauli-Weyl uncertainty principle;Donoho-Stark’s uncertainty principle

References

1. P. Ciatti, F. Ricci and M. Sundari, Heisenberg-Pauli-Weyl uncertainty inequalities and poly- nomial volume growth, Adv. Math. Vol:215 (2007), 616-625.
2. M. Cowling and J.F. Price, Bandwidth versus time concentration: the Heisenberg-Pauli-Weyl inequality, SIAM J. Math. Anal. Vol:15 (1984), 151-165.
3. D.L. Donoho and P.B. Stark, Uncertainty principles and signal recovery, SIAM J. Appl. Math. Vol:49, No.3 (1989), 906-931.
4. C.F. Dunkl, Integral kernels with reflection group invariance, Canad. J. Math. Vol:43 (1991), 1213-1227.
5. C.F. Dunkl, Hankel transforms associated to finite reflection groups, Contemp. Math. Vol:138 (1992), 123-138.
6. I.I. Hirschman, A note on entropy, Amer. J. Math. Vol:79 (1957), 152-156.
7. M.F.E.de Jeu, The Dunkl transform, Invent. Math. Vol:113 (1993), 147-162.
8. M. R¨osler, An uncertainty principle for the Dunkl transform, Bull. Austral. Math. Soc. Vol:59 (1999), 353-360.

9. N. Shimeno, A note on the uncertainty principle for the Dunkl transform, J. Math. Sci. Univ. Tokyo Vol:8 (2001), 33-42.
10. E.M. Stein, Interpolation of linear operators, Trans. Amer. Math. Soc. Vol:83 (1956), 482-492.
11. E.M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton
12. Univ. Press., Princeton, N.J, 1971.
13. Department of Mathematics, Faculty of Science, Jazan University, P.O.Box 114,
14. Jazan, Kingdom of Saudi Arabia