Reference : Some remarks to the formal and local theory of the generalized Dhombres functional eq...
 Document type : Scientific journals : Article Discipline(s) : Physical, chemical, mathematical & earth Sciences : Mathematics To cite this reference: http://hdl.handle.net/10993/11448
 Title : Some remarks to the formal and local theory of the generalized Dhombres functional equation Language : English Author, co-author : 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] Publication date : 2013 Journal title : Results in Mathematics [=RM] Publisher : Springer - Birkhäuser Volume : 63 Issue/season : 1-2 Pages : 377-395 Peer reviewed : Yes (verified by ORBilu) Audience : International ISSN : 1422-6383 e-ISSN : 1420-9012 City : Basel Country : Switzerland Keywords : [en] Complex Functional Equations Abstract : [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. Target : Researchers Permalink : http://hdl.handle.net/10993/11448 DOI : 10.1007/s00025-011-0203-0 Other URL : http://link.springer.com/article/10.1007/s00025-011-0203-0

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