Paley-Wiener-Schwartz Theorem and Microlocal Analysis in Theory of Tempered Ultrahyperfunctions

Details Paley-Wiener-Schwartz Theorem and Microlocal Analysis in Theory of Tempered Ultrahyperfunctions Paley-Wiener-Schwartz Theorem and Microlocal Analysis in Theory of Tempered Ultrahyperfunctions

2006-10-21

arxiv.org/abs/math-ph/0610051v1

PoSIC2006:047,2006

Physics

Mathematical Physics

Contribution to the Fifth International Conference on Mathematical Methods in Physics, Rio de Janeiro, April 24-28, 2006. PoS

Scientific paper

We give some precisions on the Fourier-Laplace transform theorem for tempered ultrahyperfunctions introduced by Sebasti\~ao e Silva and Hasumi, by considering the theorem in its simplest form: the equivalence between support properties of a distribution in a closed convex cone and the holomorphy of its Fourier-Laplace transform in a suitable tube with conical basis. We establish a generalization of Paley-Wiener-Schwartz theorem for this setting. This theorem is interesting in connection with the microlocal analysis, where a description of the singularity structure of tempered ultrahyperfunctions in terms of the concept of analytic wave front set is given. We also suggest a physical application of the results obtained in the construction and study of field theories with fundamental length.

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