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Sbornik: Mathematics, 2011, Volume 202, Issue 7, Pages 971–1000
DOI: https://doi.org/10.1070/SM2011v202n07ABEH004173 (Mi sm7708) 		 
This article is cited in 19 scientific papers (total in 19 papers)

One-parameter semigroups of analytic functions, fixed points and the Koenigs function

V. V. Goryainov, O. S. Kudryavtseva

The Volzhsky Institute of Humanities
English version PDF (394 kB) Citations (19) Russian version article
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DOI: https://doi.org/10.1070/SM2011v202n07ABEH004173
Abstract: Analogues of the Berkson-Porta formula for the infinitesimal generator of a one-parameter semigroup of holomorphic maps of the unit disc into itself are obtained in the case when, along with a Denjoy-Wolff point, there also exist other fixed points. With each one-parameter semigroup a so-called Koenigs function is associated, which is a solution, common for all elements of the one-parameter semigroup, of a certain functional equation (Schröder's equation in the case of an interior Denjoy-Wolff point and Abel's equation in the case of a boundary Denjoy-Wolff point). A parametric representation for classes of Koenigs functions that takes account of the Denjoy-Wolff point and other fixed points of the maps in the one-parameter semigroup is presented.
Bibliography: 19 titles.
Keywords: one-parameter semigroup, infinitesimal generator, fixed points, fractional iterates, Koenigs function.
Received: 09.03.2010
Bibliographic databases:
Document Type: Article
UDC: 517.54
MSC: 30D05
Language: English
Original paper language: Russian
Citation: V. V. Goryainov, O. S. Kudryavtseva, “One-parameter semigroups of analytic functions, fixed points and the Koenigs function”, Sb. Math., 202:7 (2011), 971–1000
Citation in format AMSBIB
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\by V.~V.~Goryainov, O.~S.~Kudryavtseva
\paper One-parameter semigroups of analytic functions, fixed points and the Koenigs function
\jour Sb. Math.
\yr 2011
\vol 202
\issue 7
\pages 971--1000
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\crossref{https://doi.org/10.1070/SM2011v202n07ABEH004173}
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  • https://www.mathnet.ru/eng/sm/v202/i7/p43
    • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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