[複變] 一題證明題

[chiehfu ( Hate)]

D = {z: |Re(z)| < 1, |Im(z)| < 1}

suppose f(z) is a function analytic on D and such that f(z) = 0

on the side of D: f(z) = 0 on Re(z)=1, -1<Im(z)<1

Consider g(z) = f(z)f(iz)f(-z)f(-iz)

prove that f is identically zero in D


請問這題該怎麼證明

謝謝....

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◆ From: 173.70.12.25
推 yusd24      :g(z) 是???
→ chiehfu     :g(z)就是那樣定義了...
推 yusd24      :可是這個問題跟 g 無關..
忘了打hint...
hint: Show that g must vanish on the boundary of the entire square,

and then recall the max. modulus theorom for analytic functions.
※ 編輯: chiehfu         來自: 173.70.12.25         (05/09 11:28)
推 yusd24      :這樣不就已經做完了嗎@@?
→ chiehfu     :不知道該怎麼起頭呀@"@