  A careful analysis of differential renormalization shows that a distinguished
choice of renormalization constants allows for a mathematically more
fundamental interpretation of the scheme. With this set of a priori fixed
integration constants differential renormalization is most closely related to
the theory of generalized functions. The special properties of this scheme are
illustrated by application to the toy example of a free massive bosonic theory.
Then we apply the scheme to the phi^4-theory. The two-point function is
calculated up to five loops. The renormalization group is analyzed, the
beta-function and the anomalous dimension are calculated up to fourth and fifth
order, respectively.
