On modelling of singularities and their products in Colombeau algebra G(R)

2010/07/09 by Blagovest Damyanov, Damyanov, Blagovest · 1 citation
Mathematics · #46F10 #46F30 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46F10 #msc:46F30

paper · pdf · doi:10.48550/arxiv.1007.1568

arxiv created 2010/07/09 · arxiv updated 2010/07/12

Abstract

Modelling of singularities given by discontinuous functions or distributions by means of generalized functions has proved useful in many problems posed by physical phenomena. We introduce in a systematic way generalized functions of Colombeau that model singularities given by distributions with singular point support. Moreover, we evaluate various products of such generalized models whenever the results admit associated distributions. The results obtained follow the idea of a well-known result of Jan Mikusinski on balancing of singular distributional products.

Cited by

• Results on modelling and products of singularities in Colombeau algebra G(R)

Related

• Results on modelling and products of singularities in Colombeau algebra G(R)
• On balanced products of the distributions x_±^a in Colombeau algebra \EuScriptG(ℝ)
• Balanced Colombeau products of the distributions x_±^-p and x^-p
• Microlocal properties of basic operations in Colombeau algebras
• Hölder-Zygmund regularity in algebras of generalized functions