Real Paley-Wiener theorems associated with the weinstein operator

Abstract

In this paper we use real analysis techniques to establish a new real Paley-Wiener theorems for the Fourier-Bessel transform associated with the Weinstein operator. More precisely we characterize the C∞-functions whose image under the Fourier-Bessel transform are functions with compact support through an Lp growth condition, p ∈ [1, +∞] and we give another version of the real Paley-Wiener theorem for L2-functions.