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Entire Solutions Of The Functional Equation f(f(z)) = g(z)

Published online by Cambridge University Press:  20 November 2018

W. J. Thron
W. J. Thron*
Affiliation:
University of Colorado
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In this note it is proved that: the functional equation

(1) f(f(z)) = g(z),

where g{z) is an entire function of finite order, which is not a polynomial, and which takes on a certain value p only a finite number of times, does not have a solution f(z) which is an entire function.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 47 - 48
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Hadamard, J., Two works on iteration and related questions, Bull. Amer. Math. Soc, 50 (1944), 67–75.Google Scholar
2. Isaacs, R., Iterates of fractional order, Can. J. Math., 2 (1950), 409–416.Google Scholar
3. Kneser, H., Reelle analytische Lösungen der Gleichung und verwandter Funktionalgleichungen, J. reine angew. Math., 187 (1950), 56–67.Google Scholar
4. Pólya, G., On an integral function of an integral function, J. London Math. Soc, 1 (1926), 12–15.Google Scholar
5. Titchmarsh, E. C., The Theory of Functions (2nd ed., Oxford, 1939).Google Scholar