GENERALIZED FOURIER-DUNKL TRANSFORM OF (; )-GENERALIZED DUNKL LIPSCHITZ FUNCTIONS

Year 2016, Volume: 4 Issue: 1, 179 - 184, 01.04.2016

R. Daher , S. El Ouadıh , M. El Hamma

https://izlik.org/JA39GJ87BL

Abstract

Using a generalized translation operator, we obtain an analog of Younis Theorem 5.2 in [5] for the generalized Fourier-Dunkl transform for func- tions satisfying the (; )-generalized Dunkl Lipschitz condition in the space L2 ;n.

Keywords

Dierential-dierence operator , Generalized Fourier-Dunkl transform , Generalized translation operator

References

• [1] S. A. Al Sadhan, R. F. Al Subaie and M. A. Mourou, Harmonic Analysis Associated with A First-Order Singular Dierential-Dierence Operator on the Real Line. Current Advances in Mathematics Research, 1,(2014), 23-34.
• [2] E. S. Belkina and S. S. Platonov, Equivalence of K-Functionnals and Modulus of Smooth- ness Constructed by Generalized Dunkl Translations, Izv. Vyssh. Uchebn. Zaved. Mat., No. 8(2008), 3-15.
• [3] C. F. Dunkl, Dierential-Dierence Operators Associated to Re ection Groups. Transactions of the American Mathematical Society, 311,(1989), 167-183.
• [4] C. F. Dunkl, Hankel Transforms Associated to Finite Re ection Groups. Contemporary Math- ematics, 138,(1992), 128- 138.
• [5] M. S. Younis, Fourier transforms of Dini-Lipschitz Functions. Int. J. Math. Math. Sci. 9 (2),(1986), 301312. doi:10.1155/S0161171286000376.
• [6] R. F. Al Subaie and M. A. Mourou, Inversion of Two Dunkl Type Intertwining Operators on R Using Generalized Wavelets. Far East Journal of Applied Mathematics, 88,(2014), 91-120.