Ambiguities in the configuration space treatment of a singular integral equation in phisup(4) theory

It is constructed the solution to a linearized Dyson equation for the IPI two-point function in lambdaphisup(2) phisup(2)-theory, where phi denotes a massless field. Special attention is given to the ambiguities arising in a conventional configuration space treatment. It is shown that proper account has to be taken of these ambiguities if one is to avoid serious discrepancies with regard to the anomalous dimension of phi. The connection between our nonperturbative result and perturbation theory as well as the cut off dependence of the solution are also discussed