Further results on Colombeau product of distributions (Q1936002)

Summary: Results on the Colombeau product of distributions \(x^{-r-1/2}_{+}\) and \(x^{-r-1/2}_{-}\) are derived. They are obtained in the Colombeau differential algebra \(\mathcal G({\mathbb R})\) of generalized functions that contains the space \(\mathcal D'({\mathbb R})\) of Schwartz distributions as a subspace and has a notion of ``association'' that is a faithful generalization of the weak equality in \(\mathcal D'({\mathbb R})\).