Results on generalized models and singular products of distributions in the Colombeau algebra $\mathcal{G}(\mathbb R)$

Commentationes mathematicae Universitatis Carolinae

Blagovest Damyanov¹ 

关键词: Colombeau algebra;    singular products of distributions;   

DOI  :  10.14712/1213-7243.2015.114

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

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 of a well-known result of Jan Mikusi\'nski on balancing of singular distributional products.

【 授权许可】

CC BY