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The fourier-borel transform in infinitely many dimensions and applications

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Functional Analysis, Holomorphy, and Approximation Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 843))

Abstract

We study the Fourier-Borel transform in the case of infinite dimensional holomorphic functions. We first show (th.1) under a very general assumption on the space E that the image of K′ (E) through the Fourier-Borel transform is the space ℑ(E) introduced in [8],

When the space E has some additional properties of nuclearity th. 1 is improved in th. 3 which generalizes a result of Boland [1]. Th. 3 is used in the section 6 of this paper where we obtain a general result (th. 4) on the approximation of solutions of some infinite dimensional convolution equations. This th. 4 unifies and improves some results of [1] and [3].

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Authors and Affiliations

  1. UER de Mathématiques et d'Informatique Université de Bordeaux I, 351, Cours de la Libération, 33405, Talence, France

    J. F. Colombeau & B. Perrot

Authors
  1. J. F. Colombeau
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  2. B. Perrot
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Silvio Machado

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© 1981 Springer-Verlag

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Colombeau, J.F., Perrot, B. (1981). The fourier-borel transform in infinitely many dimensions and applications. In: Machado, S. (eds) Functional Analysis, Holomorphy, and Approximation Theory. Lecture Notes in Mathematics, vol 843. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089273

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  • DOI: https://doi.org/10.1007/BFb0089273

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  • Print ISBN: 978-3-540-10560-2

  • Online ISBN: 978-3-540-38529-5

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