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 mailto [Karl-Franzens-Universität (Graz) > Institut of Mathematics and Scientific Computing]
Tomaschek, Jörg mailto [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 ORBilu)
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

File(s) associated to this reference

Fulltext file(s):

FileCommentaryVersionSizeAccess
Limited access
postprint_product_solutions.pdfAuthor postprint336.59 kBRequest a copy

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.