Christoph Kopper
On the local Borel transform of Perturbation Theory
(94K, Latex)

ABSTRACT.  We prove existence of the local Borel transform 
for the perturbative series of massive $\vp_4^4$-theory. 
As compared to previous proofs in the literature, the present 
bounds are much sharper as regards the dependence on 
external momenta, they are explicit in the number of external 
legs, and they are obtained quite simply through a judiciously 
chosen induction hypothesis applied to the Wegner-Wilson-Polchinski 
flow equations. We pay attention not to generate an astronomically 
large numerical constant for the inverse radius of convergence 
of the Borel transform.