On the Harmonic Analysis Associated to the Bessel-Struve Operator

TL;DR

This paper introduces the Bessel-Struve transform, establishes its inversion, characterizes its range, and proves a Schwartz-Paley-Wiener theorem, advancing harmonic analysis related to this operator.

Contribution

It provides the first comprehensive analysis of the Bessel-Struve transform, including inversion, range characterization, and a Schwartz-Paley-Wiener theorem, which are novel contributions.

Findings

Inversion theorem for the Bessel-Struve transform established.

Range characterization of the Bessel-Struve transform on Schwartz functions.

Schwartz-Paley-Wiener theorem proved for the Bessel-Struve transform.

Abstract

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