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Fine asymptotics of Christoffel functions for general measures


Author: Elliot Findley
Journal: Trans. Amer. Math. Soc. 363 (2011), 4553-4568
MSC (2010): Primary 30E10
DOI: https://doi.org/10.1090/S0002-9947-2011-05132-9
Published electronically: April 19, 2011
MathSciNet review: 2806683
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Elliot Findley
Email: marty0801@gmail.com

DOI: https://doi.org/10.1090/S0002-9947-2011-05132-9
Received by editor(s): October 7, 2008
Received by editor(s) in revised form: March 2, 2009, April 20, 2009, and May 21, 2009
Published electronically: April 19, 2011
Additional Notes: This research was partially supported by NSF grant NSF DMS 0700471.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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