Research Article

DINI LIPSCHITZ FUNCTIONS FOR THE GENERALIZED FOURIER-DUNKL TRANSFORM IN THE SPACE $L_{\alpha,n}^{2}$

Volume: 5 Number: 1 April 1, 2017
EN

DINI LIPSCHITZ FUNCTIONS FOR THE GENERALIZED FOURIER-DUNKL TRANSFORM IN THE SPACE $L_{\alpha,n}^{2}$

Abstract

Using a generalized translation operator, we obtain an analog of Younis Theorem 5.2 in [5] for the generalized Fourier-Dunkl transform for functions satisfying the Fourier-Dunkl Dini Lipschitz condition in the space $L_{\alpha,n}^{2}$.

Keywords

References

  1. [1] Al Sadhan, S.A., Al Subaie, R.F. and Mourou, M.A. Harmonic Analysis Associated with A First-Order Singular Differential-Difference Operator on the Real Line. Current Advances in Mathematics Research, 1,(2014), 23-34.
  2. [2] E.S. Belkina and S.S. Platonov, Equivalence of K-Functionnals and Modulus of Smoothness Constructed by Generalized Dunkl Translations, Izv. Vyssh. Uchebn. Zaved. Mat., 8,(2008), 3-15.
  3. [3] Dunkl, C.F. Differential-Difference Operators Associated to Reflection Groups. Transactions of the American Mathematical Society, 311,(1989), 167-183.
  4. [4] Dunkl, C.F. Hankel Transforms Associated to Finite Reflection Groups. Contemporary Mathematics, 138,(1992), 128- 138.
  5. [5] Younis M.S. Fourier transforms of Dini-Lipschitz Functions. Int. J. Math. Math. Sci. 9 (2),(1986), 301312. doi:10.1155/S0161171286000376.
  6. [6] Al Subaie, R.F. and Mourou, M.A. Inversion of Two Dunkl Type Intertwining Operators on R Using Generalized Wavelets. Far East Journal of Applied Mathematics, 88,(2014), 91-120.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

S. El Ouadıh
Departement of Mathematics, Faculty of Sciences $A\"{\i}n$ Chock, University Hassan II, Casablanca
Morocco

R. Daher
Departement of Mathematics, Faculty of Sciences $A\"{\i}n$ Chock, University Hassan II, Casablanca
Morocco

M. El Hamma This is me
Departement of Mathematics, Faculty of Sciences $A\"{\i}n$ Chock, University Hassan II, Casablanca
Morocco

Publication Date

April 1, 2017

Submission Date

February 17, 2017

Acceptance Date

August 23, 2016

Published in Issue

Year 2017 Volume: 5 Number: 1

APA
Ouadıh, S. E., Daher, R., & Hamma, M. E. (2017). DINI LIPSCHITZ FUNCTIONS FOR THE GENERALIZED FOURIER-DUNKL TRANSFORM IN THE SPACE $L_{\alpha,n}^{2}$. Konuralp Journal of Mathematics, 5(1), 92-98. https://izlik.org/JA42NX23MN
AMA
1.Ouadıh SE, Daher R, Hamma ME. DINI LIPSCHITZ FUNCTIONS FOR THE GENERALIZED FOURIER-DUNKL TRANSFORM IN THE SPACE $L_{\alpha,n}^{2}$. Konuralp J. Math. 2017;5(1):92-98. https://izlik.org/JA42NX23MN
Chicago
Ouadıh, S. El, R. Daher, and M. El Hamma. 2017. “DINI LIPSCHITZ FUNCTIONS FOR THE GENERALIZED FOURIER-DUNKL TRANSFORM IN THE SPACE $L_{\alpha,n}^{2}$”. Konuralp Journal of Mathematics 5 (1): 92-98. https://izlik.org/JA42NX23MN.
EndNote
Ouadıh SE, Daher R, Hamma ME (April 1, 2017) DINI LIPSCHITZ FUNCTIONS FOR THE GENERALIZED FOURIER-DUNKL TRANSFORM IN THE SPACE $L_{\alpha,n}^{2}$. Konuralp Journal of Mathematics 5 1 92–98.
IEEE
[1]S. E. Ouadıh, R. Daher, and M. E. Hamma, “DINI LIPSCHITZ FUNCTIONS FOR THE GENERALIZED FOURIER-DUNKL TRANSFORM IN THE SPACE $L_{\alpha,n}^{2}$”, Konuralp J. Math., vol. 5, no. 1, pp. 92–98, Apr. 2017, [Online]. Available: https://izlik.org/JA42NX23MN
ISNAD
Ouadıh, S. El - Daher, R. - Hamma, M. El. “DINI LIPSCHITZ FUNCTIONS FOR THE GENERALIZED FOURIER-DUNKL TRANSFORM IN THE SPACE $L_{\alpha,n}^{2}$”. Konuralp Journal of Mathematics 5/1 (April 1, 2017): 92-98. https://izlik.org/JA42NX23MN.
JAMA
1.Ouadıh SE, Daher R, Hamma ME. DINI LIPSCHITZ FUNCTIONS FOR THE GENERALIZED FOURIER-DUNKL TRANSFORM IN THE SPACE $L_{\alpha,n}^{2}$. Konuralp J. Math. 2017;5:92–98.
MLA
Ouadıh, S. El, et al. “DINI LIPSCHITZ FUNCTIONS FOR THE GENERALIZED FOURIER-DUNKL TRANSFORM IN THE SPACE $L_{\alpha,n}^{2}$”. Konuralp Journal of Mathematics, vol. 5, no. 1, Apr. 2017, pp. 92-98, https://izlik.org/JA42NX23MN.
Vancouver
1.S. El Ouadıh, R. Daher, M. El Hamma. DINI LIPSCHITZ FUNCTIONS FOR THE GENERALIZED FOURIER-DUNKL TRANSFORM IN THE SPACE $L_{\alpha,n}^{2}$. Konuralp J. Math. [Internet]. 2017 Apr. 1;5(1):92-8. Available from: https://izlik.org/JA42NX23MN
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