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In this paper, we introduce the Bessel-Struve transform, we establish aninversion theorem of the Weyl integral transform associated with thistransform, in the case of half integers, we give a characterization of therange of $\mathcal{D}(\mathbb{R})$ by Bessel-Struve transform and we prove aSchwartz-Paley-Wiener theorem on $\mathcal{E}'(\mathbb{R})$.

On the Harmonic Analysis Associated to the Bessel-Struve Operator