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Linear fractional transformation

  1. Mar 19, 2012 #1
    The following comes from the complex analysis text by Joseph Bak:



    He is trying to determine all conformal mappings f of upper half plane H onto the unit disk.

    "Let us first assume that f is an LFT and f(a)=0 for Im(a)>0.
    Then, since the real axis is mapped into the unit circle, it follows by Schwarz Principle of reflection that f(a*)=Infinity, so that...

    Here a* denotes the conjugate of a.

    I am having difficulty following how the Schwarz Reflection Principle is applied...and we get that f(a*)=Infinity.

    thank you.

    Also, Isn't true that the inverse Caylet Transform map the unit circle into real axis.If so, why "there is no non-constant analytic function in the unit disk that is real valued on the unit circle" ?
    Thank you
     
  2. jcsd
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