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Unformatted text preview: n =0 a n z n be analytic in the unit disk U = { z :  z  < 1 } with f (0) = 0 and f (0) = 1. Prove that if n =2 n  a n  1, then f is onetoone in U . 7. (20) Suppose that f ( z ) is analytic in the disk { z :  z  < R } ( R > 1) except for a simple pole at z = 1 with residue 1. If its Taylor expansion in the unit disk is f ( z ) = X n =0 a n z n , prove that a n 1 as n . 1...
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This document was uploaded on 01/25/2012.
 Spring '09
 Math

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