Displaying similar documents to “Balanced Colombeau products of the distributions x ± - p and x - p ”

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 ) ,...

Core functions and core divergences of regular distributions

Zdeněk Fabián, Igor Vajda (2003)

Kybernetika

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On bounded or unbounded intervals of the real line, we introduce classes of regular statistical families, called Johnson families because they are obtained using generalized Johnson transforms. We study in a rigorous manner the formerly introduced concept of core function of a distribution from a Johnson family, which is a modification of the well known score function and which in a one-to-one manner represents the distribution. Further, we study Johnson parametrized families obtained...