Dunkl–Weinstein Multiplier Operators and Applications to Reproducing Kernel Theory

Abstract

In this paper, we have interested on the Dunkl–Weinstein multiplier operators \(\mathscr {M}_{k,\beta ,a}\) on the Dunkl–Weinstein-type Paley–Wiener space \(\mathscr {H}_s\). We give for these operators an application to the reproducing kernel theory; and we deduce for them best approximation on the Paley–Wiener space \(\mathscr {H}_s\). Finally, we give two applications in two particular cases, the first is a Weinstein case \((k=0)\), and the second is the Dunkl case when \(G=\mathbb {Z}_2^d\). More precisely, we write the solution of the Tikhonov regularization problem in these cases as a convolution product of two functions.