Representation of functions as the Post-Widder inversion operator of generalized functions (Q1068326)

The authors study the Post-Widder inversion operator with respect to a class of generalized functions and distributional convergence. Necessary and sufficient conditions are obtained for a function to be represented as the rth. operate of the Post-Widder inversion operator for generalized functions. These distribution results follow after the authors define the relevant test function and generalized function spaces and obtain a classical inversion theory for the Post-Widder inversion operator applied to functions.