A Note on Fourier-Laplace Transform and Analytic Wave front Set in Theory of Tempered Ultrahyperfunctions

Details A Note on Fourier-Laplace Transform and Analytic Wave front Set in Theory of Tempered Ultrahyperfunctions A Note on Fourier-Laplace Transform and Analytic Wave front Set in Theory of Tempered Ultrahyperfunctions

2005-10-24

arxiv.org/abs/math-ph/0510082v2

J.Math.Anal.Appl. 325: 819-829, 2007

Physics

Mathematical Physics

Revised version. Accepted to be published in Journal of Mathematical Analysis and Applications

Scientific paper

10.1016/j.jmaa.2006.01.082

In this paper we study the Fourier-Laplace transform of tempered ultrahyperfunctions introduced by Sebasti\~ao e Silva and Hasumi. We establish a generalization of Paley-Wiener-Schwartz theorem for this setting. This theorem is interesting in connection with the microlocal analysis. For this reason, the paper also contains a description of the singularity structure of tempered ultrahyperfunctions in terms of the concept of analytic wave front set.

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