On the functional equation $f(p(z))=g(q(z))$, where~$p$ and~$q$ are ``generalized'' polynomials and~$f$ and~$g$ are meromorphic functions
Izvestiya. Mathematics , Tome 60 (1996) no. 5, pp. 963-984
Voir la notice de l'article provenant de la source Math-Net.Ru
We find all the solutions of the equation $f(p(z))=g(q(z))$, where $p$ and $q$ are polynomials and $p$ and $q$ are transcendental meromorphic functions in $\mathbb C$. In fact, a more general algebraic problem is solved.
@article{IM2_1996_60_5_a5,
author = {S. A. Lysenko},
title = {On the functional equation $f(p(z))=g(q(z))$, where~$p$ and~$q$ are ``generalized'' polynomials and~$f$ and~$g$ are meromorphic functions},
journal = {Izvestiya. Mathematics },
pages = {963--984},
publisher = {mathdoc},
volume = {60},
number = {5},
year = {1996},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1996_60_5_a5/}
}
TY - JOUR AU - S. A. Lysenko TI - On the functional equation $f(p(z))=g(q(z))$, where~$p$ and~$q$ are ``generalized'' polynomials and~$f$ and~$g$ are meromorphic functions JO - Izvestiya. Mathematics PY - 1996 SP - 963 EP - 984 VL - 60 IS - 5 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IM2_1996_60_5_a5/ LA - en ID - IM2_1996_60_5_a5 ER -
%0 Journal Article %A S. A. Lysenko %T On the functional equation $f(p(z))=g(q(z))$, where~$p$ and~$q$ are ``generalized'' polynomials and~$f$ and~$g$ are meromorphic functions %J Izvestiya. Mathematics %D 1996 %P 963-984 %V 60 %N 5 %I mathdoc %U http://geodesic.mathdoc.fr/item/IM2_1996_60_5_a5/ %G en %F IM2_1996_60_5_a5
S. A. Lysenko. On the functional equation $f(p(z))=g(q(z))$, where~$p$ and~$q$ are ``generalized'' polynomials and~$f$ and~$g$ are meromorphic functions. Izvestiya. Mathematics , Tome 60 (1996) no. 5, pp. 963-984. http://geodesic.mathdoc.fr/item/IM2_1996_60_5_a5/