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Complex analysis question

  1. Jun 18, 2011 #1
    1. The problem statement, all variables and given/known data


    If an analytic function vanishes on the boundary of a closed disc in its domain
    , show it vanishes on the full disc
    2. Relevant equations

    CR equations?

    3. The attempt at a solution

    Not sure how to start this one.
     
  2. jcsd
  3. Jun 18, 2011 #2

    micromass

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    Hi Metric_space! :smile:

    Have you seen the identity theorem for holomorphic functions. This says

    Did you see something like that? It would immediately give you the answer...
     
  4. Jun 18, 2011 #3
    Interesting ...I'll reread my notes. Thanks!
     
  5. Jun 18, 2011 #4

    Dick

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    You could also use the Cauchy Integral Formula, which is almost certainly in your notes even if micromass' theorem isn't.
     
  6. Jun 21, 2011 #5
    Is it just as simple as applying the Cauchy Integral formula?

    ie. it follows directly from the CIF?
     
  7. Jun 22, 2011 #6

    HallsofIvy

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    Well, what does the Cauchy Integral Formula say? What if you take the integral to be around the boundary of that disk?
     
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