A First Course in Complex Analysis · Problem 8.4.35

Taylor and Laurent Series — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis

Problem

Let hh be holomorphic in a region GG and suppose Re(h(z))≤0\text{Re}(h(z)) \leq 0 for all z∈Gz \in G, with equality at some point. Show that hh is constant.

Browse the problem library