Algebras of generalized functions with smooth parameter dependence

Details Algebras of generalized functions with smooth parameter dependence Algebras of generalized functions with smooth parameter dependence

2010-10-27

arxiv.org/abs/1010.5752v1

Mathematics

Functional Analysis

19 pages

Scientific paper

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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