ON THE EQUATION P(f) = Q(g), WHERE P, Q ARE POLYNOMIALS AND f, g ARE ENTIRE FUNCTIONS

In 1922 Ritt described polynomial solutions of the functional equation P(f) = Q(g). In this paper we describe solutions of the equation above in the case when P, Q are polynomials while f, g are allowed to be arbitrary entire functions. In fact, we describe solutions of the more general functional e...

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Bibliographic Details
Published in:American journal of mathematics Vol. 132; no. 6; pp. 1591 - 1607
Main Author: Pakovich, F.
Format: Journal Article
Language:English
Published: Baltimore, MD Johns Hopkins University Press 01.12.2010
Subjects:
Algebra
Applied mathematics
Difference and functional equations, recurrence relations
Entire functions
Exact sciences and technology
Finite differences and functional equations
Functions of a complex variable
General mathematics
General, history and biography
Infinity
Mathematical analysis
Mathematical functions
Mathematical problems
Mathematical theorems
Mathematical transformations
Mathematics
Meromorphic functions
Numerical analysis
Numerical analysis. Scientific computation
Polynomials
Rational functions
Sciences and techniques of general use
Uniqueness
Polynomial function
Strong uniqueness
Functional equation
Polynomial equation
Entire function
Rational function
Arbitrary function
ISSN:0002-9327, 1080-6377, 1080-6377
Online Access:Get full text
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Summary:In 1922 Ritt described polynomial solutions of the functional equation P(f) = Q(g). In this paper we describe solutions of the equation above in the case when P, Q are polynomials while f, g are allowed to be arbitrary entire functions. In fact, we describe solutions of the more general functional equation s = P(f) = Q(g), where s, f, g are entire functions and P, Q are arbitrary rational functions. As an application we solve the problem of description of "strong uniqueness polynomials" for entire functions.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:0002-9327
1080-6377
1080-6377
DOI:10.1353/ajm.2010.a404142