Tauberian properties for monomial summability with applications to Pfaffian systems

TL;DR

This paper investigates the incompatibility of monomial summability processes for different monomials, and applies this understanding to analyze solutions of Pfaffian systems with normal crossings, emphasizing the role of complete integrability.

Contribution

It establishes the non-compatibility of monomial summability processes for different monomials and explores their implications for Pfaffian systems with normal crossings.

Findings

Monomial summability processes are incompatible unless the series converges.

Complete integrability influences solutions of Pfaffian systems with normal crossings.

The study clarifies the limitations of summability methods in complex differential systems.

Abstract

In this paper we will show that monomial summability processes with respect to different monomials are not compatible, except in the (trivial) case of a convergent series. We will apply this fact to the study of solutions of Pfaffian systems with normal crossings, focusing in the implications of the complete integrability condition on these systems.