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Construction of Convex Mappings of p-Balls in ℂ2

Construction of Convex Mappings of p-Balls in ℂ2 For $2\leq p<\infty$ , we consider convex biholomorphic mappings F of the p-ball $B_p = \{(z,w)\in {\rm C}^2:|z|^{p}+|w|^{p}<1\}$ . In particular, we find conditions under which functions of the form $F(z,w)=(z+aw^{k},w)$ , where $a\in{\rm C}$ and $k\in{\rm N}$ , and $F(z,w)=(f(z),g(w))$ , where f and g are mappings of the unit disk, map B p onto convex domains in C2. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Construction of Convex Mappings of p-Balls in ℂ2

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Publisher
Springer Journals
Copyright
Copyright © 2004 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321052
Publisher site
See Article on Publisher Site

Abstract

For $2\leq p<\infty$ , we consider convex biholomorphic mappings F of the p-ball $B_p = \{(z,w)\in {\rm C}^2:|z|^{p}+|w|^{p}<1\}$ . In particular, we find conditions under which functions of the form $F(z,w)=(z+aw^{k},w)$ , where $a\in{\rm C}$ and $k\in{\rm N}$ , and $F(z,w)=(f(z),g(w))$ , where f and g are mappings of the unit disk, map B p onto convex domains in C2.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 7, 2013

References