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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 and Alex Sherman
Vol. 8 (2015), No. 4, 571–592
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Abstract |
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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 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. |
Keywords
OPUC, classical analysis, approximation theory, orthogonal
polynomials on the unit circle
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Mathematical Subject Classification 2010
Primary: 42C05
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Milestones
Received: 22 January 2014
Accepted: 19 August 2014
Published: 23 June 2015
Communicated by Sever S. Dragomir
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Authors |
| John Hoffman | |
| University of
Wisconsin-Madison Madison, WI 53706 United States |
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| McKinley Meyer | |
| Department of Applied and Natural
Sciences University of Wisconsin-Green Bay 2420 Nicolet Drive Green Bay, WI 54311 United States |
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| Mariya Sardarli | |
| Princeton University Princeton, NJ 08544 United States |
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| Alex Sherman | |
| University of
Wisconsin-Madison Madison, WI 53706 United States |
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