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Title: Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R
Authors: Ben Salem, N.
Ould Ahmed Salem, A.
Selmi, B.
Keywords: Jacobi-Dunkl Operator
Mean Periodic Function
Jacobi-Dunkl Expansion
Pompeiu Problem
Issue Date: 2006
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 9, No 3, (2006), 215p-236p
Abstract: Using a convolution structure on the real line associated with the Jacobi-Dunkl differential-difference operator Λα,β given by: Λα,βf(x) = f'(x) + ((2α + 1) coth x + (2β + 1) tanh x) { ( f(x) − f(−x) ) / 2 }, α ≥ β ≥ −1/2 , we define mean-periodic functions associated with Λα,β. We characterize these functions as an expansion series intervening appropriate elementary functions expressed in terms of the derivatives of the eigenfunction of Λα,β. Next, we deal with the Pompeiu type problem and convolution equations for this operator.
Description: 2000 Mathematics Subject Classification: 34K99, 44A15, 44A35, 42A75, 42A63
ISSN: 1311-0454
Appears in Collections:2006

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