Result on Colombeau product of generalized functions containing delta distribution

Abstract

In this paper we consider product of infinitely differentiable function and the r-th derivative od Dirak delta distribution. The product is obtained in Colombeau algebra of generalized functions, which is the most relevant algebraic construction for dealing with Schwartz distributions. Colombeau product of distributions generalizes classical products of distributions, but also allows us to obtain products of distributions that do not exist in the classical theory of distributions.