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Vanishing Theorems in Colombeau Algebras of Generalized Functions
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- Journal:
- Canadian Mathematical Bulletin / Volume 51 / Issue 4 / 01 December 2008
- Published online by Cambridge University Press:
- 20 November 2018, pp. 618-626
- Print publication:
- 01 December 2008
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- Article
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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.
