Results on Balanced Products of Distributions in Colombeau Algebra

Abstract

Various products of distributions with coinciding point singularities are derived when the products are ’balanced’ so that their sum is a generalized function which is associated to a distribution. These products follow the idea of a known result on distributional products published by Jan Mikusinski in 1966. The results in the present paper are obtained in the Colombeau algebra of generalized functions, which provides an efficient tool for dealing with nonlinear problems of Schwartz distributions.