Question: (4) Let U continuous map such that |f(z)| =1 for |2| = 1, |f(2)| < 1 for |2| < 1 and f is holomorphic

(4) Let U continuous map such that |f(z)| =1 for |2| =

(4) Let U continuous map such that |f(z)| =1 for |2| = 1, |f(2)| < 1 for |2| < 1 and f is holomorphic on U. Let zo be any point on the unit circle z| = 1. Prove that there is an e > 0 a such that f admits a holomorphic extension to the disk |z zo| < e. Hint: Consider log f(2) for z near zo. D be the unit disk centered at 0 and let f: U C be -

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