A Schwarz Lemma for the Symmetrized Bidisc |
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| Authors: | Agler J; Young N J |
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| Institution: | Department of Mathematics, University of California San Diego, La Jolla, CA 92093, USA
Department of Mathematics, University of Newcastle Newcastle upon Tyne NE1 7RU |
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| Abstract: | Let  be an analytic function from D to the symmetrized bidisc
 We show that if (0) = (0,0) and ( ) = (s, p) in the interiorof  , then
 Moreover, the inequality is sharp: we give an explicit formulafor a suitable in the event that the inequality holds withequality. We show further that the inverse hyperbolic tangentof the left-hand side of the inequality is equal to both theCaratheodory distance and the Kobayashi distance from (0,0)to (s, p) in int |
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