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Series Solution of a Functional Equation

Published online by Cambridge University Press:  09 April 2009

W. Pranger
W. Pranger
Affiliation:
Illinois Institute of Technology, and DePaul University, Chicago
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In this we will study analytic solutions to the linear functional equation where f and h are given functions, x is a given complex number and the function g is to be found. This is a generalization of Schröder's functional equation. The results obtained are global in nature and the solutions holomorphic. The equation will be viewed from the standpoint of linear operator theory. When studied in this manner one arrives at a general operator inversion formula.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 5 , Issue 1 , February 1965 , pp. 48 - 55
Copyright
Copyright © Australian Mathematical Society 1965

References

[1]Menger, K., Calculus a Modern Approach Ginn, (Boston, 1955).Google Scholar
[2]Heins, M., On iteration of functions which are analytic and single-valued in a given multiply-connected region, Amer. Jour. Math. 63, 381–480 (1941).CrossRefGoogle Scholar
[3]Fatou, P., Sur équations fonctionnelles, Bull. Soc. Math. France 47, 161–271 (1919); 48, 33–94, 208–314 (1920).Google Scholar
[4]Walsh, J., The Location of Critical Points of Analytic and Harmonic functions, (Amer. Math. Soc. Publ. 34, New York, 1950).Google Scholar
[5]Julia, G., Séries des fractions rationelles d'itération, C. R. Acad. Sci. Paris 180, 563 (1925).Google Scholar
[6]de, Rham G., Sur un example de fonction continue sans dérivee, Enseignment Math. (2), 3, 72–77 (1957).Google Scholar
[7]McKiernan, M., On the convergence of series of iterates, Publ. Math. Debrecen 10, 30–39 (1963).CrossRefGoogle Scholar