Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-20T10:19:17.916Z Has data issue: false hasContentIssue false
  • English
  • Français

On the functional equation F(A(z)) = G(B(z)), where A,B are polynomials and F,G are continuous functions

Published online by Cambridge University Press:  01 September 2007

F. PAKOVICH
F. PAKOVICH*
Affiliation:
Department of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, Beer Sheva 84105, Israel.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we describe solutions of the equation: F(A(z)) = G(B(z)), where A,B are polynomials and F,G are continuous functions on the Riemann sphere.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 2 , September 2007 , pp. 469 - 472
Copyright
Copyright © Cambridge Philosophical Society 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Eremenko, A. and Rubel, L.. The arithmetic of entire functions under composition. Adv. Math. 124 no. 2 (1996), 334–354.CrossRefGoogle Scholar
[2]Lysenko, S.. On the functional equation f(p(z))=g(q(z)), where p and q are “generalized” polynomials and f and g are meromorphic functions. Izv. Math. 60 no. 5 (1996), 963–984.CrossRefGoogle Scholar
[3]Pakovich, F.. On polynomials sharing preimages of compact sets, and related questions. preprint, math.DS/0603452. To appear in Geom. Funct. Anal.Google Scholar
[4]Ritt, J.. Prime and composite polynomials. Trans. Amer. Math. Soc. 23 no. 1 (1922), 51–66.CrossRefGoogle Scholar
[5]Schinzel, A.. Polynomials with special regard to reducibility. Encyclopedia Math. Appl. 77 (Cambridge University Press, 2000).Google Scholar