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

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.