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On the size of the polynomials orthonormal on the unit circle with respect to a measure which is a sum of the Lebesgue measure and $ P$ point masses


Author: S. Denisov
Journal: Proc. Amer. Math. Soc. 144 (2016), 1029-1039
MSC (2010): Primary 42C05
DOI: https://doi.org/10.1090/proc/12976
Published electronically: November 20, 2015
MathSciNet review: 3447657
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Abstract: For the measures on the unit circle that are equal to the sum of Lebesgue measure and $ p$ point masses, we give an estimate on the size of the corresponding orthonormal polynomials. As a simple corollary of the method, we obtain a bound for some exponential polynomials.


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Additional Information

S. Denisov
Affiliation: Department of Mathematics, University of Wisconsin–Madison, 480 Lincoln Dr., Madison, Wisconsin 53706
Email: denissov@math.wisc.edu

DOI: https://doi.org/10.1090/proc/12976
Received by editor(s): November 13, 2014
Published electronically: November 20, 2015
Additional Notes: The author’s research was supported by NSF grant DMS-1067413, RScF-14-21-00025, and by the IdEx Bordeaux Visiting Professor Scholarship (2014)
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2015 American Mathematical Society