214 research outputs found
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
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