Modelling and Products of Singularities in Colombeau's Algebra

Abstract

Modelling of singularities given by discontinuous functions or Schwartz distributions by means of generalized functions of Colombeau has proved useful in many problems posed by physical phenomena. We introduce in a systematic way generalized functions that model singularities given by distributions with singular point support. Moreover, we evaluate various products of singularity-modelling generalized functions whenever the result admits an associated distribution.