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Convergence of power series along vector fields and their commutators; a Cartan-Kähler type theorem

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Jakubczyk B.

Annales Polonici Mathematici

2000

tom 74

nr 1

117-132

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.

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1 Annales Polonici Mathematici

1 Jakubczyk B.

1 2000

Wyniki wyszukiwania

Convergence of power series along vector fields and their commutators; a Cartan-Kähler type theorem