Clark Measures
Using results of Agler, Aleksandrov and Doubtsov we study Clark measures determined by rational inner functions Φ(Z), of degree (n,1) on the two torus T2=∂D2. In particular in considering the Clark measure σa arising from the equation
Re((a+Φ(Z))/(a−Φ(Z))≡∫T2P(Z,ζ)dσa(ζ),
where , Z∈D2,ζ∈T2,a∈T, we obtain functions Ba, and Wa , defined on T for which the following equation holds for f∈L2(dσa),
∫T2f(ζ)dσ(ζ)=∫Tf((ζ,¯Ba(ζ))Wa(ζ)dm(ζ)+m∑k=1Cak∫Tf(τk,ζ)dm(ζ).
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