Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R
Fractional calculus and applied analysis, Tome 9 (2006) no. 3, pp. 215-236
Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library
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.
Keywords:
Jacobi-Dunkl Operator, Mean Periodic Function, Jacobi-Dunkl Expansion, Pompeiu Problem
@article{FCAA_2006_9_3_a1,
author = {Ben Salem, N. and Ould Ahmed Salem, A. and Selmi, B.},
title = {Mean-Periodic {Functions} {Associated} with the {Jacobi-Dunkl} {Operator} on {R}},
journal = {Fractional calculus and applied analysis},
pages = {215--236},
publisher = {mathdoc},
volume = {9},
number = {3},
year = {2006},
language = {en},
url = {http://geodesic.mathdoc.fr/item/FCAA_2006_9_3_a1/}
}
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 SP - 215 EP - 236 VL - 9 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FCAA_2006_9_3_a1/ LA - en ID - FCAA_2006_9_3_a1 ER -
%0 Journal Article %A Ben Salem, N. %A Ould Ahmed Salem, A. %A Selmi, B. %T Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R %J Fractional calculus and applied analysis %D 2006 %P 215-236 %V 9 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/FCAA_2006_9_3_a1/ %G en %F FCAA_2006_9_3_a1
Ben Salem, N.; Ould Ahmed Salem, A.; Selmi, B. Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R. Fractional calculus and applied analysis, Tome 9 (2006) no. 3, pp. 215-236. http://geodesic.mathdoc.fr/item/FCAA_2006_9_3_a1/