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Kernel theorems in spaces of tempered generalized functions

Published online by Cambridge University Press:  01 May 2007

ANTOINE DELCROIX
ANTOINE DELCROIX*
Affiliation:
Laboratoire AOC, Faculté des Sciences, Université des Antilles et de la Guyane, Campus de Fouillole, 97159 Pointe-à-Pitre, Guadeloupe (France). e-mail: [email protected]
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Abstract

In analogy to the classical isomorphism between and , we show that a large class of moderate linear mappings acting between the space of Colombeau rapidly decreasing generalized functions and the space of temperate ones admits generalized integral representations, with kernels belonging to . Furthermore, this result contains the classical one.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 3 , May 2007 , pp. 557 - 572
Copyright
Copyright © Cambridge Philosophical Society 2007

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