Vol. 8, No. 4, 2015

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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
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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Keywords
OPUC, classical analysis, approximation theory, orthogonal polynomials on the unit circle
Mathematical Subject Classification 2010
Primary: 42C05
Milestones
Received: 22 January 2014
Accepted: 19 August 2014
Published: 23 June 2015

Communicated by Sever S. Dragomir
Authors
John Hoffman
University of Wisconsin-Madison
Madison, WI 53706
United States
McKinley Meyer
Department of Applied and Natural Sciences
University of Wisconsin-Green Bay
2420 Nicolet Drive
Green Bay, WI 54311
United States
Mariya Sardarli
Princeton University
Princeton, NJ 08544
United States
Alex Sherman
University of Wisconsin-Madison
Madison, WI 53706
United States