Vol. 8, No. 4, 2015

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
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.

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