Colombeau products of distributions

Springerplus. 2016 Nov 29;5(1):2042. doi: 10.1186/s40064-016-3742-8. eCollection 2016.

Abstract

In this paper, some products of distributions are derived. The results are obtained in Colombeau algebra of generalized functions, which is the most relevant algebraic construction for dealing with Schwartz distributions. Colombeau algebra [Formula: see text] contains the space [Formula: see text] of Schwartz distributions as a subspace, and has a notion of 'association' that allows us to evaluate the results in terms of distributions.

Keywords: Colombeau algebra; Colombeau generalized functions; Distributions; Multiplication of distributions.