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

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  • Carlo Bardaro
  • Paul L. Butzer
  • Ilaria Mantellini
  • Gerhard Schmeisser

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.

Suggested Citation

  • Carlo Bardaro & Paul L. Butzer & Ilaria Mantellini & Gerhard Schmeisser, 2017. "A fresh approach to the Paley–Wiener theorem for Mellin transforms and the Mellin–Hardy spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 290(17-18), pages 2759-2774, December.
    • Handle: RePEc:bla:mathna:v:290:y:2017:i:17-18:p:2759-2774
    DOI: 10.1002/mana.201700043
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