S. A. Denisov, “On the problem by Steklov in the class of weight that are positive and continuous on the circle”, Keldysh Institute preprints, 2016,098, 10 pp.

On the problem by Steklov in the class of weight that are positive and continuous on the circle

S. A. Denisov^ab

^a Keldysh Institute for Applied Mathematics, Russian Academy of Sciences Miusskaya pl. 4, 125047 Moscow, RUSSIA
^b University of Wisconsin–Madison, Mathematics Department, 480 Lincoln Dr., Madison, WI, 53706, USA

Abstract: In this paper, we obtain the lower bounds for the uniform norm of the polynomials orthonormal on the unit circle with respect to a continuous and positive weight. Our bounds are sharp and improve similar results obtained earlier by M. Ambroladze.

Keywords: Uniform norm, polynomials orthonormal on the unit circle, problem of Steklov.

UDC: 517.53+517.9

DOI: 10.20948/prepr-2016-98