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Schwartz kernel theorem in algebras of generalized functions

Volume 88 / 2010

Banach Center Publications 88 (2010), 285-296 MSC: 46F10, 46F30, 47B34, 47G10. DOI: 10.4064/bc88-0-23

Abstract

A new approach to the generalization of Schwartz's kernel theorem to Colombeau algebras of generalized functions is given. It is based on linear maps from algebras of classical functions to algebras of generalized ones. In particular, this approach enables one to give a meaning to certain hypotheses in preceding similar work on this theorem. Results based on the properties of $G^{\infty}$-generalized functions class are given. A straightforward relationship between the classical and the generalized versions of Schwartz's kernel theorem is established.

Authors

• Vincent ValmorinDépartement de Mathématiques et Informatique
Université des Antilles et de la Guyane
Campus de Fouillole
97159 Pointe à Pitre Cedex, France
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