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

Yıl 2016, Cilt: 4 Sayı: 1, 179 - 184, 01.04.2016

R. Daher S. El Ouadıh M. El Hamma

Öz

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.

Anahtar Kelimeler

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

Kaynakça

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• [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.