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...

Results on generalized models and singular products of distributions in the Colombeau algebra 𝒢 ( ℝ )

Blagovest Damyanov (2015)

Commentationes Mathematicae Universitatis Carolinae

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Models of singularities given by discontinuous functions or distributions by means of generalized functions of Colombeau have proved useful in many problems posed by physical phenomena. In this paper, we introduce in a systematic way generalized functions that model singularities given by distributions with singular point support. Furthermore, we evaluate various products of such generalized models when the results admit associated distributions. The obtained results follow the idea...