# Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R

Ben Salem, N.; Ould Ahmed Salem, A.; Selmi, B.

Fractional Calculus and Applied Analysis (2006)

- Volume: 9, Issue: 3, page 215-236
- ISSN: 1311-0454

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topBen Salem, N., Ould Ahmed Salem, A., and Selmi, B.. "Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R." Fractional Calculus and Applied Analysis 9.3 (2006): 215-236. <http://eudml.org/doc/11272>.

@article{BenSalem2006,

abstract = {2000 Mathematics Subject Classification: 34K99, 44A15, 44A35, 42A75, 42A63Using 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.},

author = {Ben Salem, N., Ould Ahmed Salem, A., Selmi, B.},

journal = {Fractional Calculus and Applied Analysis},

keywords = {Jacobi-Dunkl Operator; Mean Periodic Function; Jacobi-Dunkl Expansion; Pompeiu Problem; Jacobi-Dunkl operator; mean periodic function; Jacobi-Dunkl expansion; Pompeiu problem},

language = {eng},

number = {3},

pages = {215-236},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R},

url = {http://eudml.org/doc/11272},

volume = {9},

year = {2006},

}

TY - JOUR

AU - Ben Salem, N.

AU - Ould Ahmed Salem, A.

AU - Selmi, B.

TI - Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R

JO - Fractional Calculus and Applied Analysis

PY - 2006

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 9

IS - 3

SP - 215

EP - 236

AB - 2000 Mathematics Subject Classification: 34K99, 44A15, 44A35, 42A75, 42A63Using 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.

LA - eng

KW - Jacobi-Dunkl Operator; Mean Periodic Function; Jacobi-Dunkl Expansion; Pompeiu Problem; Jacobi-Dunkl operator; mean periodic function; Jacobi-Dunkl expansion; Pompeiu problem

UR - http://eudml.org/doc/11272

ER -

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