Results on the Colombeau Products of the Distribution x + −r−1/2 with the Distributions x − −k−1/2 and x − k−1/2
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.
Key wordsdistribution Colombeau algebra Colombeau generalized functions multiplication of distributions
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