Internal sets and internal functions in Colombeau theory

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.

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Veröffentlicht in:arXiv.org 2007-07
Hauptverfasser: Oberguggenberger, M, Vernaeve, H
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Functional Analysis
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Zusammenfassung: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0707.0994