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Vanishing Theorems in Colombeau Algebras of Generalized Functions

Published online by Cambridge University Press:  20 November 2018

V. Valmorin
V. Valmorin*
Affiliation:
Département Math-Info, Université des Antilles et de la Guyane, Campus de Fouillole: 97159 Pointe à Pitre Cedex, France. e-mail: vincent.valmorin@univ-ag.fr
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Abstract

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Using a canonical linear embedding of the algebra ${{G}^{\infty }}\left( \Omega \right)$ of Colombeau generalized functions in the space of $\overline{\mathbb{C}}$ -valued $\mathbb{C}$-linear maps on the space $D\left( \Omega \right)$ of smooth functions with compact support, we give vanishing conditions for functions and linear integral operators of class ${{G}^{\infty }}$ . These results are then applied to the zeros of holomorphic generalized functions in dimension greater than one.

Keywords

32A6045P0546F30Colombeau generalized functionslinear integral operatorsgeneralized holomorphic functions
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 4 , 01 December 2008 , pp. 618 - 626
Copyright
Copyright © Canadian Mathematical Society 2008

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