arXiv subjects

H. Vernaeve

Publications and source records attributed to H. Vernaeve.

2 recordsLinked to original sources

arXiv2016

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

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.

math.FA↗

arXiv2007

Internal sets and internal functions in Colombeau theory

Inspired by nonstandard analysis, we define and study internal subsets and internal functions in algebras of Colombeau generalized functions. We prove a saturation principle for internal sets and provide applications to Colombeau algebras.

math.FA↗