Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R
2000 Mathematics Subject Classification: 34K99, 44A15, 44A35, 42A75, 42A63 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...