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manuscripta mathematica

, Volume 24, Issue 2, pp 133–171 | Cite as

Die Nuklearität der Ultradistributionsräume und der Satz vom Kern I

  • Hans-Joachim Petzsche
Article

Abstract

This article is concerned with ultradistribution spaces in the sense of Komatsu. For these spaces several tensor product theorems, especially Schwartz's kernels theorem for ultradistributions, are proved. Criteria which ensure that a nuclear locally convex space has an absolute basis are given and used to represent the spaces of periodic ultradifferential functions as Köthe sequence spaces. These results permit to state conditions on a sequence {Mp} which are equivalent to nuclearity, s-nuclearity or-as will be shown in part II-even λ-nuclearity of the corresponding ultradistribution spaces. Under some natural conditions the Beurling ultradistribution spaces defined by Komatsu are shown to constitute a proper subclass of those introduced by Beurling.

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Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Hans-Joachim Petzsche
    • 1
  1. 1.Mathematisches Institut der Universität DüsseldorfDüsseldorfBundesrepublik Deutschland

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