Characterization of Colombeau generalized functions by their pointvalues

A new characterization of elements of Colombeau - type algebras of generalized functions is presented. Since Colombeau functions are not uniquely determined by their pointvalues as defined in [1], [2], a concept of generalized points suitable for securing such a pointvalue description is introduced. This characterization provides an affirmative answer to an open question in the theory of algebras of generalized functions and enables a direct transfer of methods from classical analysis to generalized functions.