Maximal polynomial subordination to univalent functions in the unit disk |
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Authors: | Vladimir V Andrievskii Stephan Ruscheweyh |
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Institution: | 1. Institute for Applied Mathematics and Mechanics of the Ukrainian Academy of Sciences, ul. Rozy Luxemburg 74, 340114, Donetsk, Ukraine 2. Mathematisches Institut, Universit?t Würzburg, D-97074, Würzburg, Germany
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Abstract: | Let ![OHgr](/content/P15X368554U85745/xxlarge937.gif) C be a simply connected domain, 0![isin](/content/P15X368554U85745/xxlarge8712.gif) , and let n,n N, be the set of all polynomials of degree at mostn. By n( ) we denote the subset of polynomials p ![isin](/content/P15X368554U85745/xxlarge8712.gif) n withp(0)=0 andp(D)![sub](/content/P15X368554U85745/xxlarge8834.gif) , whereD stands for the unit disk {z: |z|<1}, and=" by=">1},>we denote the maximal range of these polynomials. Letf be a conformal mapping fromD onto ,f(0)=0. The main theme of this note is to relate n (or some important aspects of it) to the imagesf
s
(D), wheref
s
(z):=f(1–s)z], 0s<1. for=" instance=" we=" prove=" the=" existence=" of=" a=" universal=">1.>c
0 such that, forn 2c
0, |
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Keywords: | AMS classification" target="_blank">AMS classification 30G35 41A10 |
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