Displaying similar documents to “A contribution to the equivalence results for the product of distributions”

Results on Colombeau product of distributions

Blagovest Damyanov (1997)

Commentationes Mathematicae Universitatis Carolinae

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The differential ℂ -algebra 𝒢 ( ℝ m ) of generalized functions of J.-F. Colombeau contains the space 𝒟 ' ( ℝ m ) of Schwartz distributions as a ℂ -vector subspace and has a notion of ‘association’ that is a faithful generalization of the weak equality in 𝒟 ' ( ℝ m ) . This is particularly useful for evaluation of certain products of distributions, as they are embedded in 𝒢 ( ℝ m ) , in terms of distributions again. In this paper we propose some results of that kind for the products of the widely used distributions x ± a and δ ( p ) ( x ) ,...

Taylor formula for distributions

Bogdan Ziemian

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CONTENTS0. Introduction................................................................................................................................................................51. Preliminary remarks...................................................................................................................................................62. Hyperfunctions and their generalizations.................................................................................................................103....

Balanced Colombeau products of the distributions x ± - p and x - p

Blagovest Damyanov (2005)

Czechoslovak Mathematical Journal

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Results on singular products of the distributions x ± - p and x - p for natural p are derived, when the products are balanced so that their sum exists in the distribution space. These results follow the pattern of a known distributional product published by Jan Mikusiński in 1966. The results are obtained in the Colombeau algebra of generalized functions, which is the most relevant algebraic construction for tackling nonlinear problems of Schwartz distributions.