The Golinskii-Ibragimov Method and a Theorem of Damanik and Killip
نویسنده
چکیده
In 1971, Golinskii and Ibragimov proved that if the Verblunsky coefficients, {αn}n=0, of a measure dμ on ∂D obey ∑∞ n=0 n|αn| < ∞, then the singular part, dμs, of dμ vanishes. We show how to use extensions of their ideas to discuss various cases where ∑N n=0 n|αn| diverges logarithmically. As an application, we provide an alternative to a part of the proof of a recent theorem of Damanik and Killip.
منابع مشابه
Verblunsky coefficients with Coulomb-type decay
We also consider the monic orthogonal polynomials Φn(z). They obey the Szegő recursion Φn+1(z) = zΦn(z)− αnΦn(z), where Φn(z) = z Φn(1/z). The αn are called Verblunsky coefficients and they belong to the unit disk D = {z ∈ C : |z| < 1}. Conversely, every α ∈ ×n=0D corresponds to a unique measure. See [14, 15, 16] for background material on orthogonal polynomials on the unit circle (OPUC). In th...
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