Between the Paley-Wiener theorem and the Bochner tube theorem

Volume 60 / 1995

Zofia Szmydt, Bogdan Ziemian Annales Polonici Mathematici 60 (1995), 299-304 DOI: 10.4064/ap-60-3-299-304

Abstract

We present the classical Paley-Wiener-Schwartz theorem [1] on the Laplace transform of a compactly supported distribution in a new framework which arises naturally in the study of the Mellin transformation. In particular, sufficient conditions for a function to be the Mellin (Laplace) transform of a compactly supported distribution are given in the form resembling the Bochner tube theorem [2].

Authors

  • Zofia Szmydt
  • Bogdan Ziemian

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