Article (Scientific journals)
Some remarks to the formal and local theory of the generalized Dhombres functional equation
Reich, Ludwig; TOMASCHEK, Jörg
2013In Results in Mathematics, 63 (1-2), p. 377-395
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Keywords :
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.
Disciplines :
Mathematics
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
Language :
English
Title :
Some remarks to the formal and local theory of the generalized Dhombres functional equation
Publication date :
2013
Journal title :
Results in Mathematics
ISSN :
1420-9012
Publisher :
Springer - Birkhäuser, Basel, Switzerland
Volume :
63
Issue :
1-2
Pages :
377-395
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 20 November 2013

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