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Poisson kernel

  1. Jul 14, 2012 #1
    1. The problem statement, all variables and given/known data

    show that the integral of the poisson kernel (1-r^2)/(1-2rcos(x)+r^2) converges to 0 uniformly in x as r tend to 1 from the left ,on any closed subinterval of [-pi,pi] obtained by deleting a middle open interval (-a,a)

    2. Relevant equations

    the integral of poisson kernel from -pi to pi is 2pi

    . The attempt at a solution
    :it must by a direct conclusion of the integral in 2 but somehow i fail to see it.
  2. jcsd
  3. Nov 2, 2012 #2
    Is ##r## always positive? Is ##P(-r,x)## defined?
  4. Nov 2, 2012 #3
    main guidelines for the proof in the attachment.

    Attached Files:

    • 001.jpg
      File size:
      25.7 KB
  5. Nov 2, 2012 #4
    I am hedipaldi but i did not pause this question.How come it is on my name??
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