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A fresh approach to the Paley-Wiener theorem for Mellin transforms and the Mellin-Hardy spaces (1706.00285v1)
Published 1 Jun 2017 in math.FA
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.