Geodesic
A new version of circular symmetrization with applications to $p$-valent functions
Sbornik. Mathematics, Tome 203 (2012) no. 7, pp. 996-1011

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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. 
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     author = {V. N. Dubinin},
     title = {A new version of circular symmetrization with applications to $p$-valent functions},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
     volume = {203},
     number = {7},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2012_203_7_a3/}
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V. N. Dubinin. A new version of circular symmetrization with applications to $p$-valent functions. Sbornik. Mathematics, Tome 203 (2012) no. 7, pp. 996-1011. http://geodesic.mathdoc.fr/item/SM_2012_203_7_a3/