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

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.