Results on the Colombeau Products of the Distribution x+−r−1/2 with the Distributions x−−k−1/2 and x−k−1/2

详细

Results on the products of the distribution x₊^−r−1/2 with the distributions x₋^−k−1/2 and x₋^k−1/2 are obtained in the differential algebra G(ℝ) of Colombeau generalized functions, which contains the space D′(ℝ) of Schwartz distributions as a subspace; in this algebra the notion of association is defined, which is a faithful generalization of weak equality in G(ℝ). This enables treating the results in terms of distributions again.