Let $f:\mathbf{D}\to \mathbf{C}$ be a holomorphic function on the unit disc. Suppose that $f(0) \neq 0$ and that $\vert f\vert$ is bounded from below by some real number $C>0$ on some annulus contained in $D$. Then, does it follow that $\vert f\vert $ is bounded from below on $\mathbf{D}$ by some positive real number $C^\prime$?
Is a holomorphic function on the unit disc not vanishing at zero bounded
0
$\begingroup$
complex-analysis
-
0@Tsotsi Hint: the answer to the question in the last sentence is "No". – 2013-04-30
1 Answers
1
Try $f(z)=1-z$. $ $ $ $ $ $ $ $ $ $