An application of internal objects to microlocal analysis in generalized function algebras

We illustrate the use of internal objects in the nonlinear theory of generalized functions by means of an application to microlocal analysis in Colombeau algebras.Comment: 14 page

Characterization of distributions having a value at a point in the sense of Robinson

We characterize Schwartz distributions having a value at a single point in the sense introduced by means of nonstandard analysis by A. Robinson. They appear to be distributions continuous in a neighborhood of the point.Comment: 5 page

Strongly internal sets and generalized smooth functions

Based on a refinement of the notion of internal sets in Colombeau's theory, so-called strongly internal sets, we introduce the space of generalized smooth functions, a maximal extension of Colombeau generalized functions. Generalized smooth functions as morphisms between sets of generalized points form a sub-category of the category of topological spaces. In particular, they can be composed unrestrictedly.Comment: 17 pages, some minor correction