MathDB

12

Part of 2014 IMS

Problems(1)

Open subset of complex plane

Source: IMS 2014 - Day2 - Problem12

10/5/2014
Let UU be an open subset of the complex plane C\mathbb{C} including D={z∈C:∣z∣≤1}\mathbb{D}=\{z \in \mathbb{C} : |z| \le 1\} and ff be analytic over UU. Prove that if for every zz with a complex norm equal to 11(∣z∣=1|z|=1) we have 0<Re(zˉf(z))0<Re(\bar{z}f(z)), then ff has only one root in D\mathbb{D} and that's simple.
complex analysiscomplex analysis unsolved