Fine asymptotics of Christoffel functions for general measures

Findley, Elliot

doi:10.1090/S0002-9947-2011-05132-9

Fine asymptotics of Christoffel functions for general measures
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by Elliot Findley PDF

Trans. Amer. Math. Soc. 363 (2011), 4553-4568 Request permission

Abstract:

Let $\mu$ be a measure on the unit circle satisfying Szegő’s condition. In 1991, A. Máté calculated precisely the first-order asymptotic behavior of the sequence of Christoffel functions associated with $\mu$ when the point of evaluation lies on the circle, resolving a long-standing open problem. We extend his results to measures supported on smooth curves in the plane. In the process, we derive new asymptotic estimates for the Cesáro means of the corresponding 1-Faber polynomials and investigate some applications to orthogonal polynomials, linear ill-posed problems and the mean ergodic theorem.

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