Show that if \(f\) is a meromorphic function in \(\Delta (0;1+h)=\{z:|z|<1+h\}\), where \(h>0\), and \(|f(z)|=1\) for \(|z|=1\), then \(f\) is a rational function.
Question
Math 6210 • Real Analysis
1992 • Question 8
Question
1992 • Question 8
Show that if \(f\) is a meromorphic function in \(\Delta (0;1+h)=\{z:|z|<1+h\}\), where \(h>0\), and \(|f(z)|=1\) for \(|z|=1\), then \(f\) is a rational function.