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We first characterize the image of the compactly supported smooth evenfunctions 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 whoseq-Weinstein transform has compact support as a subspace of the space of$L_{\alpha, q, a}^{2}$-functions.

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