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Results in Mathematics

, Volume 5, Issue 1–2, pp 123–135 | Cite as

An infinite dimensional version of the Paley-Wiener-Schwartz isomorphism

  • J. F. Colombeau
  • S. Ponte
Forschungsbeiträge Research Paper

Abstract

In the infinite dimensional case it is known from a Dineen-Nachbin counterexample that the natural generalization of the Paley-Wiener-Schwartz theorem is no longer valid: The image through the Fourier transform F of the space ℰ′(E) is made of entire functions on E′ that, besides the usual inequality, satisfy a more technical condition. We define and study here a dense subspace, denoted by E(E), of ℰ(E) with a proper topology such that F (E′(E)) is made of the entire functions on E′ that satisfy only the classical inequality. For this reason this space E(E) is suited for the study of convolution and partial differential equations in spaces of C functions on locally convex spaces.

Keywords

Entire Function Separable Hilbert Space Compact Open Topology Nuclear Space Topological Isomorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 1982

Authors and Affiliations

  • J. F. Colombeau
    • 1
  • S. Ponte
    • 2
  1. 1.U.E.R. de Mathématiques et d’InformatiqueUniversité de Bordeaux 1TalenceFrance
  2. 2.Departamento de Teoria de Funciones Facultad dt MatematicasUniversidaa de SantiagoSpain

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