#### 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 ${L}_{\infty }$ 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
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