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arXiv · 1010.5752

Algebras of generalized functions with smooth parameter dependence

Annegret Burtscher·Michael Kunzinger
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Abstract

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 $\widetilde{\mathbb{K}}_{sm}$ of generalized numbers in this unified setting. In particular, we investigate the ring and order structure of $\widetilde{\mathbb{K}}_{sm}$ and establish some properties of its ideals.

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Annegret Burtscher, Michael Kunzinger. 2010-10-27. Algebras of generalized functions with smooth parameter dependence. https://doi.org/10.1017/s0013091510001410

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