Extented Paley-Wiener type theorems for the Mellin and Fourier transforms on the half-real line

Abstract

In this paper we present generalisations of Paley-Wiener type theorems to Mellin and (Laplace-)Fourier transforms of rapidly decreasing smooth functions with positive support and log-polyhomogeneous asymptotic expansion at zero. This article is based on the thesis CdC and uses results borrowed from RS, RS81, P79, FGD, P79, SZ.