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Vanishing Theorems in Colombeau Algebras of Generalized Functions

Published online by Cambridge University Press:  20 November 2018

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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2008

References

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