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.
@article{bwmeta1.element.bwnjournal-article-apmv74z1p117bwm,
author = {Jakubczyk, B.},
title = {Convergence of power series along vector fields and their commutators; a Cartan-K\"ahler type theorem},
journal = {Annales Polonici Mathematici},
volume = {75},
year = {2000},
pages = {117-132},
zbl = {0961.35023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv74z1p117bwm}
}
Jakubczyk, B. Convergence of power series along vector fields and their commutators; a Cartan-Kähler type theorem. Annales Polonici Mathematici, Tome 75 (2000) pp. 117-132. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv74z1p117bwm/
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