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

Daniel H. T. Franco·Luiz H. Renoldi
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Abstract

We give some precisions on the Fourier-Laplace transform theorem for tempered ultrahyperfunctions introduced by Sebastião 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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Daniel H. T. Franco, Luiz H. Renoldi. 2006-10-21. Paley-Wiener-Schwartz Theorem and Microlocal Analysis in Theory of Tempered Ultrahyperfunctions. https://arxiv.org/abs/math-ph/0610051

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