Complex Analysis: Theory and Applications · Problem 10.3.6

Applications of Harmonic Functions — Howell & Matthews

Mathematics — Complex Analysis · poisson-integral-formula

Problem

Let

U(t)

be a real-valued function that satisfies the conditions for Poisson's integral formula for the upper half-plane. If

U(t)

is an even function so that

U(-t) = U(t)

, then show that the harmonic function

\phi(x,y)

has the property

\phi(-x,y) = \phi(x,y)