Real Paley-Wiener Theorem for the Generalized Weinstein transform in quantum calculus

Abstract

We first characterize the image of the compactly supported smooth even functions under the q-Weinstein transform as a subspace of the Schwartz space. We then describe the space of smooth $L_{\alpha, q, a}^{2}$-functions whose q-Weinstein transform has compact support as a subspace of the space of $L_{\alpha, q, a}^{2}$-functions.