Unformatted text preview:  f j ( z )  2 on a disc centered around z (and included in U ). Then show the f j are uniformly bounded on compact sets. (4) Consider f ( z ) = 1 2 ( z + 1 /z ). Show that f gives a conformal equivalence between D (0 , 1) and C ∪{∞}\ [1 , 1]. 1 What happens with circles ∂D (0 ,r ) under this map? And what with the linesections ω [0 , 1) originating from the origin (for ω ∈ ∂D (0 , 1))? Hint: conic sections. 1 In a coincidence, this conformal map was used in a talk I went to today (after I made the problem set). 1...
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 Spring '09
 Holomorphic function, Conformal map, automorphism group Aut

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