Complex Analysis: Theory and Applications · Problem 10.3.7

Applications of Harmonic Functions — Howell & Matthews

Mathematics — Complex Analysis · poisson-integral-formula

Problem

Let U(t)U(t) be a real-valued function that satisfies the conditions for Poisson's integral formula for the upper half-plane. If U(t)U(t) is an odd function so that for all tt, U(−t)=−U(t)U(-t) = -U(t), then show that the harmonic function ϕ(x,y)\phi(x,y) has the property ϕ(−x,y)=−ϕ(x,y)\phi(-x,y) = -\phi(x,y).

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