Epstein-Glaser renormalization and differential renormalization

In the framework of causal perturbation theory by Epstein and Glaser the pr ocess of renormalization is precisely equivalent to the extension of time-o rdered distributions to coincident points. This is achieved by a modified T aylor subtraction on the corresponding test functions. I show that the pull back of this operation to the distributions yields expressions known from d ifferential renormalization. The subtraction is equivalent to BPHZ subtract ion in momentum space. Some examples from Euclidean scalar field theory in flat and curved spacetime will be presented.