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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Veröffentlicht in:	American journal of mathematics Jg. 132; H. 6; S. 1591 - 1607
1. Verfasser:	Pakovich, F.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Baltimore, MD Johns Hopkins University Press 01.12.2010
Schlagworte:	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
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Abstract	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.
AbstractList	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. [PUBLICATION ABSTRACT] 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.
Author	Pakovich, F.
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Copyright	Copyright © 2010 The Johns Hopkins University Press Copyright © 2010 The Johns Hopkins University Press. 2015 INIST-CNRS Copyright Johns Hopkins University Press Dec 2010
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SubjectTerms	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
Title	ON THE EQUATION P(f) = Q(g), WHERE P, Q ARE POLYNOMIALS AND f, g ARE ENTIRE FUNCTIONS
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