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Proving something is bounded

  1. Nov 3, 2011 #1
    Hey,

    I'm trying to prove that uv=>0 is bounded so I can state that an entire function is constant when f = u + iv, when f is entire.

    I have worked out the rest but i'm struggling to prove that its bounded,

    Can you say u=>0, v=>0 then u + v => 0, and that bounded from below?
     
  2. jcsd
  3. Nov 3, 2011 #2
    I'm not sure what you are trying to prove - is it given that u,v are harmonic & uv>=0 ?
     
  4. Nov 3, 2011 #3
    They gave

    f = u + iv is an entire function,

    that means u and v are harmonic right?

    and it asks to show f is constant if uv=>0 everywhere

    I think i have done that part just using louivilles theorem, but i realised i was just assuming u and v were bounded
     
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