Relative Szegő asymptotics for Toeplitz determinants
نویسندگان
چکیده
In this paper we study the asymptotic behavior, as n → ∞, of ratios Dn(e hdμ)/Dn(dμ) of Toeplitz determinants defined by a measure μ and a sufficiently smooth function h. The approach we follow is based on the Verblunsky coefficients associated to μ. We prove that that the second order asymptotics depends on only few Verblunsky coefficients. In particular, we establish a relative version of the Strong Szegő Limit Theorem for measures with essential support on a single arc.
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