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

Annales Polonici Mathematici (2000)

- Volume: 74, Issue: 1, page 117-132
- ISSN: 0066-2216

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topJakubczyk, B.. "Convergence of power series along vector fields and their commutators; a Cartan-Kähler type theorem." Annales Polonici Mathematici 74.1 (2000): 117-132. <http://eudml.org/doc/208360>.

@article{Jakubczyk2000,

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.},

author = {Jakubczyk, B.},

journal = {Annales Polonici Mathematici},

keywords = {control systems; Cartan-Kähler theorem; power series; convergence; commutators; Cauchy estimates; vector fields; formal and analytic vector field; analyticity of formal solution; nonlinear singular partial differential equations},

language = {eng},

number = {1},

pages = {117-132},

title = {Convergence of power series along vector fields and their commutators; a Cartan-Kähler type theorem},

url = {http://eudml.org/doc/208360},

volume = {74},

year = {2000},

}

TY - JOUR

AU - Jakubczyk, B.

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

JO - Annales Polonici Mathematici

PY - 2000

VL - 74

IS - 1

SP - 117

EP - 132

AB - 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.

LA - eng

KW - control systems; Cartan-Kähler theorem; power series; convergence; commutators; Cauchy estimates; vector fields; formal and analytic vector field; analyticity of formal solution; nonlinear singular partial differential equations

UR - http://eudml.org/doc/208360

ER -

## References

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