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Algebras of generalized functions with smooth parameter dependence

Published online by Cambridge University Press:  04 January 2012

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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2011

References

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