Convergence of power series along vector fields and their commutators; a Cartan-Kähler type theorem
Volume 74 / 2000
Annales Polonici Mathematici 74 (2000), 117-132
DOI: 10.4064/ap-74-1-117-132
Abstract
We study convergence of formal power series along families of formal or analytic vector fields. One of our results says that if a formal power series converges along a family of vector fields, then it also converges along their commutators. Using this theorem and a result of T. Morimoto, we prove analyticity of formal solutions for a class of nonlinear singular PDEs. In the proofs we use results from control theory.
