Unformatted text preview: f is constant on B (0; 1), then f is constant. b. Prove that if e f is constant on B (0; 1), then f is constant. (4) Let G ⊂ C be open and let f be holomorphic on G . Let G * = { z : ¯ z ∈ G } and deﬁne f * ( z ) = f (¯ z ) for all z ∈ G * . Prove that f * is holomorphic on G * and express f * ( z ) in terms of f . (5) (Quals ’04) Let G ⊂ C be an open and connected set and let f : G → C be a holomorphic function such that  f ( z )  = C for all z ∈ G . Prove that f is constant on G . 1...
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 Fall '11
 Schep
 Calculus, Equations, Derivative, Complex number, Holomorphic function, G. Prove

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