Internal sets and internal functions in Colombeau theory

By Michael Oberguggenberger, Hans Vernaeve. 2007

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This paper is devoted to the study of generalized functions as pointwise functions (so-called internal functions) on certain sets of generalized points (so-called internal sets). We treat the case of the Colombeau algebras of generalized functions, for which these notions have turned out to constitute a fundamental technical tool. We provide general foundations for the notion of internal functions and internal sets and prove a saturation principle. Various applications to Colombeau algebras are given.

Subfields: Mathematical Physics, Theoretical Computer Science, Philosophy

View Paper: https://www.semanticscholar.org/paper/6cfc3d8787d422801511cddd3ba1f22eddc1edc4