Reference : A remark on Schröder's equation: Formal and analytic linearization of iterative roots... |

Scientific journals : Article | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/16566 | |||

A remark on Schröder's equation: Formal and analytic linearization of iterative roots of the power series f(z)=z | |

English | |

Reich, Ludwig [] | |

Tomaschek, Jörg [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |

In press | |

Monatshefte für Mathematik | |

Springer | |

Yes (verified by ORBi^{lu}) | |

International | |

0026-9255 | |

1436-5081 | |

Vienna | |

Austria | |

[en] Schröder equation ; Linearization ; Normal forms | |

[en] We study Schröder’s equation (i.e. the problem of linearization) for local analytic functions
F with F (0)=0, F(0)=1, F(0) a root of 1. While Schröder’s equation in this case need not have even a formal solution, we show that if F is formally linearizable, then it can also be linearized by an invertible local analytic transformation. On the other hand, there exist also divergent series solutions of Schröder’s equation in this situation. We give some applications of our results to iterative functional equations, functional-differential equations and iteration groups. | |

Researchers | |

http://hdl.handle.net/10993/16566 | |

10.1007/s00605-013-0601-3 | |

http://download.springer.com/static/pdf/357/art%253A10.1007%252Fs00605-013-0601-3.pdf?auth66=1399470256_3eb6b0fdcc7012481afbe852e6f389be&ext=.pdf |

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