An extension of Borel-Laplace methods and monomial summability

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.

arXiv comment17 pages

References in corpus (1)

• Tauberian properties for monomial summability with applications to Pfaffian systems

Cited by in corpus (4)

• On parametric Gevrey asymptotics for some nonlinear initial value problems in two complex time variables
• Summability in a monomial for some classes of singularly perturbed partial differential equation
• Tauberian theorems for $k$--summability with respect to an analytic germ
• Entire functions polynomially bounded in several variables