Kudryavtseva O.S. Fractional iteration of functions analytic in the unit disk, with real coefficients

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Kudryavtseva Olga Sergeevna
 
Senior Lecturer, Chair of Applied Mathematics and Informatics, VHI Volgograd State University
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Ulitca 40 let Pobedy, 11, 404133б Volzhskii, Russian Federation

Abstract. The present paper deals with the problem of fractional iteration in a class of analytic functions mapping the unit disk into itself, preserving the origin and having real coefficients of the expansion in a Maclaurin series, in terms of the Koenigs function. An integral representation of the class of Koenigs functions which correspond to the functions of the studied class admitting fractional iteration in this class is obtained. Some necessary conditions for the existence of fractional iterates of functions of the studied class in terms of estimates of their initial coefficients are given.

Key words: fractional iterates, one-parameter semigroup, infinitesimal generator, Koenigs function, fixed points.

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Fractional iteration of functions analytic in the unit disk, with real coefficients by Kudryavtseva O.S. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. №2 (15) 2011 pp. 50-62

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