Modelling and products of singularities in Colombeau's algebra G (R)

Modeling of singularities given by discontinuos 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.