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(Solved): Problem 5 Suppose that f is an analytic function from the unit disc |z|<1|f(z)|<1 n at the or ...
Problem 5 Suppose that f is an analytic function from the unit disc |z|<1|f(z)|<1 n at the origin. Prove that
|f(z)|<=|z|^(n). Furthermore, show that if |f(a)|=|a|^(n) for some a with |a|<1, then
f(z)=\epsi lonz^(n) for some \epsi lon with |\epsi lon|=1.