Higher-Order Szego Theorems With Two Singular Points

Barry Simon, Andrej Zlatos

We consider probability measures, $dμ=w(θ) \f{dθ}{2π} +dμ_\s$, on the unit circle, $\partial\bbD$, with Verblunsky coefficients, $\{{\alpha }_j{\}}_{j=0}^{\infty }$. We prove for ${\theta }_1\ne {\theta }_2$ i…