Some approximate inversion formulas for the Whittaker multiplier operators

In this paper, we define and study the multiplier operators [Formula: see text] associated with the Whittaker operator [Formula: see text], and we introduce and study the extremal function [Formula: see text]. We deduce some approximate inversion formulas for the operators [Formula: see text], in the Whittaker–Sobolev space [Formula: see text], and in Whittaker–Paley–Wiener space [Formula: see text], respectively.