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Type: Artigo de periódico
Title: Structure Of Spaces Of C∞-functions On Nuclear Spaces
Author: Colombeau J.F.
Paques O.T.W.
Abstract: Let E be a real nuclear locally convex space; we prove that the space ℰub(E), of all C∞-functions of uniform bounded type on E, coincides with the inductive limit of the spaces ℰNbc(Ev) (introduced by Nachbin-Dineen), when V ranges over a basis of convex balanced 0-neighbourhoods in E. Let E be a real nuclear bornological vector space; we prove that the space ℰ(E) of all C∞-functions on E coincides with the projective limit of the spaces ℰNbc(EB), when B is a closed convex balanced bounded subset of E. As a consequence we obtain some density results and a version of the Paley-Wiener-Schwartz theorem. © 1983 The Weizmann Science Press of Israel.
Editor: Springer-Verlag
Rights: fechado
Identifier DOI: 10.1007/BF02760667
Date Issue: 1983
Appears in Collections:Unicamp - Artigos e Outros Documentos

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