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Convex Subordination Chains in Several Complex Variables

Published online by Cambridge University Press:  20 November 2018

Ian Graham
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada, graham@math.toronto.edu
Hidetaka Hamada
Affiliation:
Faculty of Engineering, Kyushu Sangyo University, 3-1 Matsukadai 2-Chome, Higashi-ku Fukuoka 813-8503, Japan, h.hamada@ip.kyusan-u.ac.jp
Gabriela Kohr
Affiliation:
Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1M. Kogălniceanu Str., 400084 Cluj-Napoca, Romania, gkohr@math.ubbcluj.ro
John A. Pfaltzgraff
Affiliation:
Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599-3250, USA, jap@math.unc.edu
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Abstract

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In this paper we study the notion of a convex subordination chain in several complex variables. We obtain certain necessary and sufficient conditions for a mapping to be a convex subordination chain, and we give various examples of convex subordination chains on the Euclidean unit ball in ${{\mathbb{C}}^{n}}$. We also obtain a sufficient condition for injectivity of $f(z/\|z\|,\,\,\|z\|)$ on ${{B}^{n}}\backslash \{0\}$, where $f(z,t)$ is a convex subordination chain over $(0,1)$.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2009

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