There does not exist a non-constant analytic function in the unit circle which is real valued on the unit circle.(adsbygoogle = window.adsbygoogle || []).push({});

I am not able to see why. I am trying to apply Louisville's Theorem, or maybe Open Mapping Th., but I fail.

Is there a way of extending this function so that it entire? and even then...why should it be bounded?

Thank you

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# Complex analysis non-constant analytic function

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