Title: An analyst's take on the BPHZ theorem,
Abstract: We provide a self-contained formulation of the BPHZ theorem in the Euclidean
context, which yields a systematic procedure to "renormalise" otherwise
divergent integrals appearing in generalised convolutions of functions with a
singularity of prescribed order at their origin. We hope that the formulation
given in this article will appeal to an analytically minded audience and that
it will help to clarify to what extent such renormalisations are arbitrary (or
not). In particular, we do not assume any background whatsoever in quantum
field theory and we stay away from any discussion of the physical context in
which such problems typically arise.