Regularity of nonlinear generalized functions: A counterexample in the nonstandard setting

Abstract

Regularity theory in generalized function algebras of Colombeau type is largely based on the notion of G∞-regularity, which reduces to C∞-regularity when restricted to Schwartz distributions. Surprisingly, in the nonstandard version of the Colombeau algebras, this basic property of G∞-regularity does not hold.