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.
Abstract. In this paper we will show that monomial summability can be characterized using Borel-Laplace like integral transformations depending of a parameter 0 < s < 1. We will apply this result to prove 1-summability in a monomial of formal solutions of a family of partial differential equations.
The goal of this article is to establish tauberian theorems for the k-summability processes defined by germs of analytic functions in several complex variables. The proofs are based on the tauberian theorems for k-summability in one variable and in monomials, and a method of monomialization of germs of analytic functions.Recently the notions of asymptotic expansions and k-summability in a germ of analytic function have been defined and developed systematically in [8] by the second and third authors, generalizing
The aim of this paper is to continue the study of asymptotic expansions and summability in a monomial in any number of variables, as introduced in [3, 15]. In particular, we characterize these expansions in terms of bounded derivatives and we develop Tauberian theorems for the summability processes involved. Furthermore, we develop and apply the Borel-Laplace analysis in this framework to prove the monomial summability of solutions of a specific class of singularly perturbed PDEs.
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