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Sbornik: Mathematics, 2012, Volume 203, Issue 7, Pages 996–1011
DOI: https://doi.org/10.1070/SM2012v203n07ABEH004251 (Mi sm7891) 		 
This article is cited in 14 scientific papers (total in 14 papers)

A new version of circular symmetrization with applications to $p$-valent functions

V. N. Dubinin

Far Eastern Federal University, Vladivostok
English version PDF (314 kB) Citations (14)
References:
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DOI: https://doi.org/10.1070/SM2012v203n07ABEH004251
Abstract: A new version of circular symmetrization of sets, functions and condensers is proposed, which is different from classical symmetrization in the following respect: the symmetrized sets and condensers lie on the Riemann surface of the inverse function of a Chebyshev polynomial. As applications, Hayman's well-known results for nonvanishing $p$-valent holomorphic functions are supplemented as well as results for $p$-valent functions in a disc which have a zero of order $p$ at the origin.
Bibliography: 20 titles.
Keywords: circular symmetrization, capacity of a condenser, Riemann surface, $p$-valent function, Chebyshev polynomial.
Received: 19.05.2011
Russian version:
Matematicheskii Sbornik, 2012, Volume 203, Number 7, Pages 79–94
DOI: https://doi.org/10.4213/sm7891
Bibliographic databases:
Document Type: Article
UDC: 517.54
MSC: 30A10, 30C55, 30C85
Language: English
Original paper language: Russian
Citation: V. N. Dubinin, “A new version of circular symmetrization with applications to $p$-valent functions”, Mat. Sb., 203:7 (2012), 79–94; Sb. Math., 203:7 (2012), 996–1011
Citation in format AMSBIB
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:661
    Russian version PDF:185
    English version PDF:13
    References:64
    First page:36
     
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