Algebras of generalized functions with smooth parameter dependence

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

19 pages

References in corpus (2)

• Isomorphisms of algebras of Colombeau generalized functions
• An algebraic approach to manifold-valued generalized functions

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