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Entire Functions

  1. Nov 26, 2007 #1
    let f be an entire function..

    1) prove if e^f is bounded then f is constant
    2) prove that if Re f is bounded then f is constant

    i'm guessing you would have to use suitable exponentials but i don't have a good enough idea of what to do here. any help would be greatly appreciated :Dxx
     
  2. jcsd
  3. Nov 26, 2007 #2

    Office_Shredder

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    You can start with if an entire function is bounded everywhere, it's constant.

    http://en.wikipedia.org/wiki/Liouville's_theorem_(complex_analysis)

    I think the proof moves the absolute value bars into the integral a bit prematurely (as generally a path integral of a real function can give a complex number as an answer, but I can't be bothered to check if in this case it actually comes out real all the time), but the basic idea is there
     
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