Let S C C be a domain that is bounded, and let f: SC be continuous, and f = O(U) is holomorphic. If |f| be a constant on the boundry of S, Prove that f must have a zero in S.

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Chapter2: Second-order Linear Odes
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Let S CC be a domain that is bounded, and let ƒ : S → C be continuous, and
f = O(U) is holomorphic. If |ƒ| be a constant on the boundry of S, Prove that
f must have a zero in S.
Transcribed Image Text:Let S CC be a domain that is bounded, and let ƒ : S → C be continuous, and f = O(U) is holomorphic. If |ƒ| be a constant on the boundry of S, Prove that f must have a zero in S.
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