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

Carlo Bardaro; Paul L. Butzer; Ilaria Mantellini; G. Schmeisser

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arXiv · 1706.00285

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

Carlo Bardaro·Paul L. Butzer·Ilaria Mantellini·G. Schmeisser

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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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Carlo Bardaro, Paul L. Butzer, Ilaria Mantellini, G. Schmeisser. 2017-06-01. A fresh approach to the Paley-Wiener theorem for Mellin transforms and the Mellin-Hardy spaces. https://arxiv.org/abs/1706.00285

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