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Vanishing Theorems in Colombeau Algebras of Generalized Functions |
Canad. Math. Bull. 51(2008), 618-626
Published:2008-12-01
Printed: Dec 2008
Printed: Dec 2008
- V. Valmorin
Abstract
Using a canonical linear embedding of the algebra
${\mathcal G}^{\infty}(\Omega)$ of Colombeau generalized functions in the space of
$\overline{\C}$-valued $\C$-linear maps on the space
${\mathcal D}(\Omega)$ of smooth functions with compact support, we give vanishing
conditions for functions and linear integral operators of class
${\mathcal G}^\infty$. These results are then applied to the zeros of holomorphic
generalized functions in dimension greater than one.
| Keywords: | Colombeau generalized functions, linear integral operators, generalized holomorphic functions |
| MSC Classifications: |
32A60 - Zero sets of holomorphic functions 45P05 - Integral operators [See also 47B38, 47G10] 46F30 - Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) |