Show that the family of functions \(\{z^n\}_{n\in \mathbb Z_{\ge 0}}\) form a normal family in \(|z|<1\), also in \(|z|>1\), but not in any region that contains a point on the unit circle.
Question
Math 6210 • Real Analysis
Spring 2020 • Question 10
Question
Spring 2020 • Question 10
Show that the family of functions \(\{z^n\}_{n\in \mathbb Z_{\ge 0}}\) form a normal family in \(|z|<1\), also in \(|z|>1\), but not in any region that contains a point on the unit circle.