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

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