Algebras of generalized functions with smooth parameter dependence

Annegret Burtscher, Michael Kunzinger
2012 Proceedings of the Edinburgh Mathematical Society  
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.
doi:10.1017/s0013091510001410 fatcat:tte2yzxs2vaozjufs6lcpeqtaa