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Algebras of generalized functions with smooth parameter dependence

Part of: Distributions, generalized functions, distribution spaces Nonlinear functional analysis Topological rings and modules

Published online by Cambridge University Press:  04 January 2012

Annegret Burtscher  and
Michael Kunzinger
Annegret Burtscher
Affiliation:
Department of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Wien, Austria (annegret.burtscher@univie.ac.at; michael.kunzinger@univie.ac.at)
Michael Kunzinger
Affiliation:
Department of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Wien, Austria (annegret.burtscher@univie.ac.at; michael.kunzinger@univie.ac.at)
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Abstract

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We show that spaces of Colombeau generalized functions with smooth parameter dependence are isomorphic to those with continuous parametrization. Based on this result we initiate a systematic study of algebraic properties of the ring of generalized numbers in this unified setting. In particular, we investigate the ring and order structure of and establish some properties of its ideals.

Keywords

algebras of generalized functionsColombeau algebrassmooth parametrizationalgebraic properties

MSC classification

Secondary: 46F30: Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) 13J25: Ordered rings 46T30: Distributions and generalized functions on nonlinear spaces
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 1 , February 2012 , pp. 105 - 124
Copyright
Copyright © Edinburgh Mathematical Society 2011

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