Structure of spaces ofC
∞-functions on nuclear spaces |
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Authors: | J F Colombeau O T W Paques |
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Institution: | (1) U.E.R. de Mathématiques et d’Informatique, Université de Bordeaux 1, 33.405 Talence, France;(2) Departmento de Matemática IMECC, UNICAMP, Universidade Estadual de Campinas, 13.100 Campinas, SP, Brasil |
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Abstract: | LetE be a real nuclear locally convex space; we prove that the space ℰub(E), of allC
∞-functions of uniform bounded type onE, coincides with the inductive limit of the spaces ℰNbc(E
v) (introduced by Nachbin-Dineen), whenV ranges over a basis of convex balanced 0-neighbourhoods inE. LetE be a real nuclear bornological vector space; we prove that the space ℰ(E) of allC
∞-functions onE coincides with the projective limit of the spaces ℰNbc(E
B), whenB is a closed convex balanced bounded subset ofE. As a consequence we obtain some density results and a version of the Paley-Wiener-Schwartz theorem.
Research done during the stay of this author at the University of Bordeaux (France) in the academic year 1980–1981. |
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Keywords: | |
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