  Following Epstein-Glaser's work we show how a QFT formulation based on
operator valued distributions (OPVD) with adequate test functions treats
original singularities of propagators on the diagonal in a mathematically
rigourous way.Thereby UV and/or IR divergences are avoided at any stage, only a
finite renormalization finally occurs at a point related to the arbitrary scale
present in the test functions.Some well known UV cases are examplified.The
power of the IR treatment is shown for the free massive scalar field theory
developed in the (conventionally hopeless) mass perturbation expansion.It is
argued that the approach should prove most useful for non pertubative methods
where the usual determination of counterterms is elusive
