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2015 Maximization of the size of monic orthogonal polynomials on the unit circle corresponding to the measures in the Steklov class
John Hoffman, McKinley Meyer, Mariya Sardarli, Alex Sherman
Involve 8(4): 571-592 (2015). DOI: 10.2140/involve.2015.8.571

Abstract

We investigate the size of monic, orthogonal polynomials defined on the unit circle corresponding to a finite positive measure. We find an upper bound for the L growth of these polynomials. Then we show, by example, that this upper bound can be achieved. Throughout these proofs, we use a method developed by Rahmanov to compute the polynomials in question. Finally, we find an explicit formula for a subsequence of the Verblunsky coefficients of the polynomials.

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John Hoffman. McKinley Meyer. Mariya Sardarli. Alex Sherman. "Maximization of the size of monic orthogonal polynomials on the unit circle corresponding to the measures in the Steklov class." Involve 8 (4) 571 - 592, 2015. https://doi.org/10.2140/involve.2015.8.571

Information

Received: 22 January 2014; Accepted: 19 August 2014; Published: 2015
First available in Project Euclid: 22 November 2017

zbMATH: 1319.42022
MathSciNet: MR3366011
Digital Object Identifier: 10.2140/involve.2015.8.571

Subjects:
Primary: 42C05

Rights: Copyright © 2015 Mathematical Sciences Publishers

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Vol.8 • No. 4 • 2015
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