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How to compute inner product in the Hardy space

  1. Sep 29, 2012 #1
    Let [itex]H^2[/itex] be the Hardy space on the open unit disk.
    I am wondering how can I compute the following inner product

    [itex]<\frac{1}{\left(1-\overline{\alpha_1} z\right)^2}\frac{z-\alpha_2}{1-\overline{\alpha_2} z},\frac{z}{\left(1-\overline{\alpha_1} z\right)^2}>,[/itex]

    where [itex]\alpha_1,\alpha_2[/itex] in the unit disk.

    I tried to expand the functions but it became complicated. Also it did not work with the integration.

    Is there an idea to be tried?

    Thanks in advanced
  2. jcsd
  3. Oct 1, 2012 #2
    Any idea?
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