Let \(W=\{z\mid z\in \mathbb C,\ z=x+iy\text { and }y^2-x^2<1\}\). Let \(f\) be an entire function such that \(f(\mathbb C)\subset W\). Show that \(f\) is a constant function.
Question
Math 6210 • Real Analysis
Fall 1997 • Question 7
Question
Fall 1997 • Question 7
Let \(W=\{z\mid z\in \mathbb C,\ z=x+iy\text { and }y^2-x^2<1\}\). Let \(f\) be an entire function such that \(f(\mathbb C)\subset W\). Show that \(f\) is a constant function.