On Subordination Chains with Normalization Given by a Time-dependent Linear Operator |
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Authors: | Ian Graham Hidetaka Hamada Gabriela Kohr |
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Institution: | 1. Department of Mathematics, University of Toronto, Toronto, ON, M5S 2E4, Canada 2. Faculty of Engineering, Kyushu Sangyo University, 3-1 Matsukadai 2-Chome, Higashi-ku, Fukuoka, 813-8503, Japan 3. Faculty of Mathematics and Computer Science, Babe?-Bolyai University, 1 M. Kog?lniceanu Str., 400084, Cluj-Napoca, Romania
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Abstract: | In this paper we are concerned with solutions, in particular with univalent solutions, of the Loewner differential equation
associated with non-normalized subordination chains on the Euclidean unit ball B
n
in
\mathbbCn{\mathbb{C}^n}. The main result is a generalization to higher dimensions of a well known result due to Becker. Various particular cases
of this result have been recently obtained for subordination chains with normalization Df(0,t)=etIn{Df(0,t)=e^tI_n} or Df(0, t) = e
tA
, t ≥ 0, where
A ? L(\mathbbCn,\mathbbCn){A\in L(\mathbb{C}^n,\mathbb{C}^n)}. We also determine the form of the standard solutions to the Loewner differential equation associated with generalized spirallike
mappings. In the last section we obtain the form of the solution in the presence of coefficient bounds. |
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Keywords: | |
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