Vanishing Theorems in Colombeau Algebras of Generalized Functions
Vanishing Theorems in Colombeau Algebras of Generalized Functions
Abstract Using a canonical linear embedding of the algebra of Colombeau generalized functions in the space of -valued ℂ-linear maps on the space of smooth functions with compact support, we give vanishing conditions for functions and linear integral operators of class . These results are then applied to the zeros …