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Analytic solutions of Boettcher’s functional equation in the unit disk. (English) Zbl 0526.30033
MSC:
30D05Functional equations in the complex domain, iteration and composition of analytic functions
39B99Functional equations
References:
[1]Cowen, C. C.,Iteration and the solution of functional equations for functions analytic in the unit disk. Trans. Amer. Math. Soc.265 (1981), 69–95. · doi:10.1090/S0002-9947-1981-0607108-9
[2]Koenigs, G., Recherches sur les integrales des certaines équations fonctionelles. Ann. Ec. Norm. Sup. (3)1 (1884), supplément, 3–41.
[3]Ger, J. andSmajdor, A.,Regular iteration in the case of multiplier zero. Aequationes Math.7 (1972), 127–131. · Zbl 0243.39006 · doi:10.1007/BF01818507
[4]Kuczma, M., Sur l’équation fonctionnelle de Bottcher. Mathematica (Cluj)8 (1966), 279–285.
[5]Kuczma, M., Une remarque sur les solutions analytiques d’une équation fonctionnelle. Colloq. Math.16 (1967), 93–99.
[6]Kuczma, M.,Functional equations in a single variable. Polish Scientific Publishers, Warszawa, 1968.
[7]Pommerenke, Ch.,On the iteration of analytic functions in a half plane. I. J. London Math. Soc. (2)19 (1979), 439–447. · Zbl 0405.30018 · doi:10.1112/jlms/s2-19.3.439
[8]Szekeres, G.,Regular iteration of real and complex functions. Acta Math.100 (1958), 203–258. · Zbl 0145.07903 · doi:10.1007/BF02559539
[9]Valiron, G.,Fonctions analytiques. Presses Universitaires de France, Paris, 1954.