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

B. Jakubczyk

Annales Polonici Mathematici (2000)

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

Abstract

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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.

How to cite

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Jakubczyk, 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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  18. [S2] H. J. Sussmann, unpublished manuscript. 

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