Between the Paley-Wiener theorem and the Bochner tube theorem

Zofia Szmydt; Bogdan Ziemian

Annales Polonici Mathematici (1995)

  • Volume: 60, Issue: 3, page 299-304
  • ISSN: 0066-2216

Abstract

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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].

How to cite

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Zofia Szmydt, and Bogdan Ziemian. "Between the Paley-Wiener theorem and the Bochner tube theorem." Annales Polonici Mathematici 60.3 (1995): 299-304. <http://eudml.org/doc/262396>.

@article{ZofiaSzmydt1995,
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].},
author = {Zofia Szmydt, Bogdan Ziemian},
journal = {Annales Polonici Mathematici},
keywords = {Mellin distributions; Bochner tube theorem; Paley-Wiener-Schwartz theorem; Laplace transform of a compactly supported distribution; Mellin transformation},
language = {eng},
number = {3},
pages = {299-304},
title = {Between the Paley-Wiener theorem and the Bochner tube theorem},
url = {http://eudml.org/doc/262396},
volume = {60},
year = {1995},
}

TY - JOUR
AU - Zofia Szmydt
AU - Bogdan Ziemian
TI - Between the Paley-Wiener theorem and the Bochner tube theorem
JO - Annales Polonici Mathematici
PY - 1995
VL - 60
IS - 3
SP - 299
EP - 304
AB - 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].
LA - eng
KW - Mellin distributions; Bochner tube theorem; Paley-Wiener-Schwartz theorem; Laplace transform of a compactly supported distribution; Mellin transformation
UR - http://eudml.org/doc/262396
ER -

References

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  1. [1] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer, 1985. Zbl0601.35001
  2. [2] W. Rudin, Lectures on the Edge of the Wedge Theorem, Amer. Math. Soc., Providence, 1971. 
  3. [3] Z. Szmydt and B. Ziemian, The Mellin Transformation and Fuchsian Type Partial Differential Equations, Math. Appl. 56, Kluwer, 1992. Zbl0771.35002

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