Reference : Some remarks to the formal and local theory of the generalized Dhombres functional eq... |

Scientific journals : Article | |||

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

http://hdl.handle.net/10993/11448 | |||

Some remarks to the formal and local theory of the generalized Dhombres functional equation | |

English | |

Reich, Ludwig [Karl-Franzens-Universität (Graz) > Institut of Mathematics and Scientific Computing] | |

Tomaschek, Jörg [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit > ; Karl-Franzens-Universität (Graz) > Institute of Mathematics and Scientific Computing] | |

2013 | |

Results in Mathematics [=RM] | |

Springer - Birkhäuser | |

63 | |

1-2 | |

377-395 | |

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

International | |

1422-6383 | |

1420-9012 | |

Basel | |

Switzerland | |

[en] Complex Functional Equations | |

[en] We are looking for local analytic respectively formal solutions of the generalized Dhombres
functional equation $f(zf(z))=\varphi(f(z))$ in the complex domain. First we give two proofs of the existence theorem about solutions $f$ with $f(0) = w_0$ and $w_0 \in \mathbb{C}^\star \setminus \mathbb{E}$ where $\mathbb{E}$ denotes the group of complex roots of $1$. Afterwards we represent solutions $f$ by means of infinite products where we use on the one hand the canonical convergence of complex analysis, on the other hand we show how solutions converge with respect to the weak topology. In this section we also study solutions where the initial value $z_0$ is different from zero. | |

Researchers | |

http://hdl.handle.net/10993/11448 | |

10.1007/s00025-011-0203-0 | |

http://link.springer.com/article/10.1007/s00025-011-0203-0 |

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