Further generalization of the Borel transform for the non-perturbative regime

A new generalization of the Borel transform improving the Duncan-Pernice proposal, and designed for obtaining any non perturbative contributions is presented. This new transform leads to a non-ambiguous reconstruction of the original theory. This generalized transform is applied to the analysis of a one-dimensional spin chain and the two-dimensional non-linear sigma model on the lattice. In both models the singularity structure related to renormalons is obtained