An infinite dimensional version of the Paley-Wiener-Schwartz isomorphism
type: Item
instance of: scholarly article
title: An infinite dimensional version of the Paley-Wiener-Schwartz isomorphism
zbMATH Open document ID: 0532.46010
DOI: 10.1007/BF03323309
published in: Results in Mathematics
publication date: 1982-01-01T00:00:00Z
review text: Sei E ein reeller nuklearer Raum, \({\mathcal E}(E)\) der Raum der \(C^\infty\)-Funktionen auf E. Es ist bekannt, daß der Satz von Paley-Wiener für Elemente von \({\mathcal E}'(E)\) nur unter Zusatzvoraussetzungen gilt. Verf. untersucht einen Teilraum \({\mathbb{E}}(E)\) von \({\mathcal E}(E)\), für den der Satz von Paley-Wiener in der üblichen Fassung gilt.
Mathematics Subject Classification ID: 46E25
Mathematics Subject Classification ID: 46E10
Mathematics Subject Classification ID: 46G20
zbMATH DE Number: 3844380
zbMATH Keywords: Paley-Wiener-theorem
zbMATH Keywords: nuclear space
author: J.-F. Colombeau
author: Socorro Ponte
reviewed by: Gunter Bengel
MaRDI profile type: Publication
cites work: Q4200722
cites work: Q3945059
cites work: \(C^{\infty}\) functions in infinite dimension and linear partial differential difference equations with constant coefficients
cites work: Q4768190
cites work: Holomorphic Functions on Nuclear Spaces
cites work: Q3882976
cites work: Q3933460
cites work: Entire functions of exponential type bounded on the real axis and Fourier transforms of distributions with bounded supports
cites work: Q5791009
cites work: Q3895407
full work available at URL: https://doi.org/10.1007/bf03323309
OpenAlex ID: W1995871207
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description: scientific article; zbMATH DE number 3844380