Holomorphic extension theorem for tempered ultrahyperfunctions

Franco, Daniel H. T.

doi:10.4171/PM/1839

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Portugaliae Mathematica

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Volume 66, Issue 2, 2009, pp. 175–190

DOI: 10.4171/PM/1839

Published online: 2009-06-30

Holomorphic extension theorem for tempered ultrahyperfunctions

Daniel H. T. Franco^[1]

(1) Universidade Federal de Viçosa, Brazil

In this article we are concerned with the space of tempered ultrahyperfunctions corresponding to a proper open convex cone. A holomorphic extension theorem (the version of the celebrated Edge-of-the-Wedge Theorem) will be given for this setting. As application, a version is also given of the principle of determination of an analytic function by its values on a non-empty open real set. The article finishes with the generalization of holomorphic extension theorem à la Martineau.

Keywords: Tempered ultrahyperfunctions, Edge-of-the-Wedge Theorem, Fourier–Laplace transform

Franco Daniel H.: Holomorphic extension theorem for tempered ultrahyperfunctions. Port. Math. 66 (2009), 175-190. doi: 10.4171/PM/1839