Probability measures with reflection coefficients {an} ε ζ4and {an+1- an} ε ζ2 are Erd&ohuml;s measures

Authors:
Sergey A. Denisov
Affiliations:
Faculty of Computational Mathematics and Cybernetics, Moscow State University, Vorob'evy Gory, Moscow, Russia/ and California Institute of Technology, Mathematics, 253-37, Pasadena, California
Venue:
Journal of Approximation Theory
Year:
2002

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Abstract

In this article, we consider the system of polynomials orthogonal on the unit circle. It is proved that the conditions {an} ∈ l4 and {an+1 - an} ∈ l2 imposed on the reflection parameters {an} are sufficient for the associated measure to be Erdös one.