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.References
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Additional Information
- Elliot Findley
- Email: marty0801@gmail.com
- 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.
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 4553-4568
- MSC (2010): Primary 30E10
- DOI: https://doi.org/10.1090/S0002-9947-2011-05132-9
- MathSciNet review: 2806683