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Inequality with absolute value of a complex integral

  1. Mar 6, 2009 #1
    I'm stuck trying to prove a step inside a lemma from Serre; given is


    To prove:


    I've tried using Cauchy-Schwartz for integrals, but this step is too big (using Mathematica, it lead to a contradiction); something simpler must do the trick.
    Thanks in advance.
  2. jcsd
  3. Mar 7, 2009 #2

  4. Mar 7, 2009 #3
    As far as I know, that only holds if f(x) is real, which it is not.
  5. Mar 7, 2009 #4
    It also holds for complex-valued functions. For Riemann sums this is just the triangle inequality, and in the general case one can use an approximation argument.
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