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Lookup NU author(s): Professor Jim Agler, Emeritus Professor Nicholas Young
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Let cp be an analytic function from ID to the symmetrized bidisc Gamma =(def)((lambda (1) +lambda (2), lambda (1)lambda (2)) : \ lambda (1)\ less than or equal to 1, \ lambda (2)\ less than or equal to 1). We show that if phi (0) = (0, 0) and phi(lambda) = (s, p) in the interior of Gamma, then 2 \s - p (s) over bar \+\s(2)-4p \ /4-\s \ (2) less than or equal to \ lambda \. Moreover, the inequality is sharp: we give an explicit formula for a suitable cp in the event that the inequality holds with equality. We show further that the inverse hyperbolic tangent of the left-hand side of the inequality is equal to both the Caratheodory distance and the Kobayashi distance from (0,0) to (s, p) in int Gamma.
Author(s): Agler J, Young NJ
Publication type: Article
Publication status: Published
Journal: Bulletin of the London Mathematical Society
Year: 2001
Volume: 33
Issue: 2
Pages: 175-186
Print publication date: 01/03/2001
ISSN (print): 0024-6093
ISSN (electronic): 1469-2120
Publisher: Oxford University Press
URL: http://dx.doi.org/10.1112/blms/33.2.175
DOI: 10.1112/blms/33.2.175
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