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2010 The Continuous Wavelet Transform Associated with a Differential-Difference Operator and Applications
H. Mejjaoli , N. Sraieb
Commun. Math. Anal. 9(1): 48-65 (2010).

Abstract

In this paper we consider a class of singular differential-difference operators on the real line. We define and study the continuous wavelet transform associated with these operators. We prove a Plancherel formula, an inversion formula and a weak uncertainty principle for it. As applications, we establish Calderón's formulas and give practical real inversion formula for the generalized continuous wavelet transform. At the end of the paper, analogous of Heisenberg's inequality for the generalized continuous wavelet transform on Chébli-Triméche hypergroups and a special case of Jacobi-Dunkl operator are proved.

Citation

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H. Mejjaoli . N. Sraieb . "The Continuous Wavelet Transform Associated with a Differential-Difference Operator and Applications." Commun. Math. Anal. 9 (1) 48 - 65, 2010.

Information

Published: 2010
First available in Project Euclid: 21 April 2010

zbMATH: 1189.42018
MathSciNet: MR2594682

Subjects:
Primary: 35C80
Secondary: ‎43A32, 51F15

Rights: Copyright © 2010 Mathematical Research Publishers

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Vol.9 • No. 1 • 2010
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