Unformatted text preview: C → C is holomorphic. Moreover assume there exist constants c 1 ,c 2 ,± > 0 such that  f ( z )  ≤ c 1 exp( c 2  z  1 / 2± ) for all z ∈ C , and that  f ( z )  ≤ 1 for z ∈ R ≤ . Show that f is constant. Show that f ( z ) = cos( √z ) (which is welldeﬁned by evenness of cos) satisﬁes the conditions of the problem with ± = 0, but not the conclusion. Hint: Prove a Phragm´ enLindel¨of type theorem. 1...
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This document was uploaded on 12/08/2010.
 Spring '09

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