An analog of Titchmarsh's theorem for the Laguerre–Bessel transform

Abstract

Purpose – Using a generalized translation operator, this study aims to obtain a generalization of Titchmarsh's theorem for the Laguerre–Bessel transform for functions satisfying the ψ-Laguerre–Bessel–Lipschitz condition in the space L2α (K), where K=0,+∞×0,+∞[. Design/methodology/approach – The author has employed the results developed by Titchmarsh, of reference number [1]. Findings – In this paper, an analogous of Titchmarsh's theorem is established for Laguerre–Bessel transform. Originality/value – To the best of the authors’ findings, at the time of submission of this paper, the results reported are new and interesting.

Keywords

• Laguerre–Bessel transform
• Generalized translation operator
• Lipschitz class
• Titchmarsh theorem