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 ${\mathcal{G}}^{\infty }$-regularity, which reduces to $C^{\infty }$-regularity when restricted to Schwartz distributions. Surprisingly, in the nonstandard version of the Colombeau algebras, this basic property of ${\mathcal{G}}^{\infty }$-regularity does not hold.

5 pp

References in corpus (2)

• The use of Generalised Functions and Distributions in General Relativity
• A rigorous solution concept for geodesic and geodesic deviation equations in impulsive gravitational waves