  We embed in a generalized Borel procedure the notion of renormalization and
renormalons. While there are several efforts in literature to have a
semi-classical understanding of the renormalons, here we argue that this is not
the fundamental issue and show how to deal with the problem. We find that the
effective Lagrangians describing the effects of renormalons are non-local in
space but local in time. The quark-antiquark potential in QCD with an infinite
number of fermions is also analyzed. The connection between the analyzable
functions, the Callan-Symanzyk equation and the renormalons, provides an
insight of a non-perturbative renormalization from the standard perturbative
renormalization approach.
