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smooth parametrization

Proceedings of the Edinburgh Mathematical Society (1)

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Algebras of generalized functions with smooth parameter dependence
Part of
Annegret Burtscher, Michael Kunzinger
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 55 / Issue 1 / February 2012

Published online by Cambridge University Press:

04 January 2012, pp. 105-124
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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.