Geodesic
Vanishing Theorems in Colombeau Algebras of Generalized Functions
Canadian mathematical bulletin, Tome 51 (2008) no. 4, pp. 618-626

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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.
DOI : 10.4153/CMB-2008-061-3
Mots-clés : 32A60, 45P05, 46F30, Colombeau generalized functions, linear integral operators, generalized holomorphic functions 
Valmorin, V. Vanishing Theorems in Colombeau Algebras of Generalized Functions. Canadian mathematical bulletin, Tome 51 (2008) no. 4, pp. 618-626. doi: 10.4153/CMB-2008-061-3
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     title = {Vanishing {Theorems} in {Colombeau} {Algebras} of {Generalized} {Functions}},
     journal = {Canadian mathematical bulletin},
     pages = {618--626},
     year = {2008},
     volume = {51},
     number = {4},
     doi = {10.4153/CMB-2008-061-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-061-3/}
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