If \(f(z)\) is analytic in \(|z|\le 1\) and satisfies \(|f|=1\) on \(|z|=1\), show that \(f(z)\) is rational.
Question
Math 6210 • Real Analysis
Spring 2020 • Question 9
Question
Spring 2020 • Question 9
If \(f(z)\) is analytic in \(|z|\le 1\) and satisfies \(|f|=1\) on \(|z|=1\), show that \(f(z)\) is rational.