An Inverse Function Theorem for Generalized Functions

Evelina Erlacher
(University of Vienna)

Abstract: We give a short introduction to the special Colombeau algebra of generalized functions. This algebra is a nonlinear extension of classical distribution theory and is defined as the quotient of moderate nets of smooth functions modulo negligible nets of smooth functions. We discuss several notions of invertibility of moderate nets and present a theorem providing sufficient conditions to guarantee the latter. Finally, we define (local) invertibility of an element of the special Colombeau algebra and present an inverse function theorem.