Unformatted text preview: F ( z ) = ( f ( z ) if  z  = 1 1 2 Ï€i H Î³ f ( Î¶ ) Î¶z dÎ¶ if  z  < 1 where Î³ is a curve traversing the unit circle once in positive direction. Is F continuous on D (0 , 1) = { z âˆˆ C   z  â‰¤ 1 } ? (4) Let f be holomorphic on D (0 , 1) = { z   z  < 1 } and continuous on D (0 , 1). Moreover suppose  f ( z )  â‰¤ 1 if  z  = 1. Prove that  f ( z )  â‰¤ 1 for all z âˆˆ D (0 , 1). 1...
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 Spring '09
 Calculus, positive direction

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