An example of Newton's method for an equation in Gevrey series
A generalization of the paper of \textit{T. Aoki} et al. [Adv. Stud. Pure Math. 54, 19--94 (2009; Zbl 1175.34112)], the author discusses the reduction problem for one-dimensional Schrödinger equations near a multiple turning point. Constructing a functional analytic framework based essentially on the idea of the use of Banach scales for the purpose of treating factorially divergent Gevrey series (with respect to the Planck constant) and employing Newton's method of tangents in this framework, he shows that near a multiple turning point a one-dimensional Schrödinger equation can be transformed to a canonical form by a change of independent variable, which is analytic near a point in question and factorially divergent with respect to the Planck constant.
scientific article; zbMATH DE number 6359825
scientific article