Show that there is no holomorphic function f in the unit disc D that extends continuously to |z|=1 such that f(z) =1/z for |z|=1(adsbygoogle = window.adsbygoogle || []).push({});

Some thoughts that might not be relevant:

If such f existed then, I can see that f maps the unit circle to the unit circle and the unit disc onto the unit disc.

On |z|=1 f would be equal to the conjugate function which is not differentiable anywhere.

I'm kind of stuck. I appreciate any suggestions.

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# Show the function doesnt exist

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