A First Course in Complex Analysis · Problem 6.3.9

Power Series — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · harmonic-functions

Problem

Suppose

f

is holomorphic in the region

G \subseteq \mathbb{C}

with image

H := \{f(z) : z \in G\}

, and

u

is harmonic on

H

. Show that

u(f(z))

is harmonic on

G