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A fresh approach to the Paley–Wiener theorem for Mellin transforms and the Mellin–Hardy spaces
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AbstractHere 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 ofpolar‐analytic functionin 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.
Title: A fresh approach to the Paley–Wiener theorem for Mellin transforms and the Mellin–Hardy spaces
Description:
AbstractHere 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 ofpolar‐analytic functionin 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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