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Convex Subordination Chains in Several Complex Variables

Published online by Cambridge University Press:  20 November 2018

Ian Graham ,
Hidetaka Hamada ,
Gabriela Kohr  and
John A. Pfaltzgraff
Ian Graham
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada, [email protected]
Hidetaka Hamada
Affiliation:
Faculty of Engineering, Kyushu Sangyo University, 3-1 Matsukadai 2-Chome, Higashi-ku Fukuoka 813-8503, Japan, [email protected]
Gabriela Kohr
Affiliation:
Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1M. Kogălniceanu Str., 400084 Cluj-Napoca, Romania, [email protected]
John A. Pfaltzgraff
Affiliation:
Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599-3250, USA, [email protected]
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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 $(0,1)$.

Keywords

32H0230C45biholomorphic mappingconvex mappingconvex subordination chainLoewner chainsubordination.
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 3 , 01 June 2009 , pp. 566 - 582
Copyright
Copyright © Canadian Mathematical Society 2009

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