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].
@article{bwmeta1.element.bwnjournal-article-apmv60z3p299bwm,
author = {Zofia Szmydt and Bogdan Ziemian},
title = {Between the Paley-Wiener theorem and the Bochner tube theorem},
journal = {Annales Polonici Mathematici},
volume = {62},
year = {1995},
pages = {299-304},
zbl = {0830.46034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv60z3p299bwm}
}
Zofia Szmydt; Bogdan Ziemian. Between the Paley-Wiener theorem and the Bochner tube theorem. Annales Polonici Mathematici, Tome 62 (1995) pp. 299-304. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv60z3p299bwm/
[000] [1] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer, 1985. | Zbl 0601.35001
[001] [2] W. Rudin, Lectures on the Edge of the Wedge Theorem, Amer. Math. Soc., Providence, 1971.
[002] [3] Z. Szmydt and B. Ziemian, The Mellin Transformation and Fuchsian Type Partial Differential Equations, Math. Appl. 56, Kluwer, 1992. | Zbl 0771.35002