4. Let ϕ be a real-valued piecewise continuous function on ∂D. If ϕ(eiθ ) = ϕ(e−iθ ) for all θ ∈ R, prove that ϕ has a Fourier series of the form
∼ α ∞
ϕ(eiθ ) 0 +2 αn
where the Fourier coefﬁcients are all real.
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