Paley-Wiener theorems for the Mellin transformation
CONTENTS Foreword..............................................................................................................................5 Introduction..........................................................................................................................6 1. Preliminaries....................................................................................................................7 1.1. Terminology and notation.............................................................................................7...
We present the classical Paley-Wiener-Schwartz theorem [1] on the Laplace transform of a compactly supported distribution in a new framework which arises naturally in the study of the Mellin transformation. In particular, sufficient conditions for a function to be the Mellin (Laplace) transform of a compactly supported distribution are given in the form resembling the Bochner tube theorem [2].
A class of distributions supported by certain noncompact regular sets K are identified with continuous linear functionals on . The proof is based on a parameter version of the Seeley extension theorem.
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