A fresh approach to the Paley-Wiener theorem for Mellin transforms and the Mellin-Hardy spaces

2017/06/01 by Carlo Bardaro, P. L. Butzer, Bardaro, Carlo +5
Mathematics · #44A05 #Advanced Mathematical Identities #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1706.00285

openalex publication_date 2017/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Here we give a new approach to the Paley--Wiener theorem in a Mellin analysis setting which avoids the use of the Riemann surface of the logarithm and analytical branches and is based on new concepts of "polar-analytic function" in the Mellin setting and Mellin--Bernstein spaces. A notion of Hardy spaces in the Mellin setting is also given along with applications to exponential sampling formulas of optical physics.

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