Fejer convolutions for an extremal problem in the Steklov class

Abstract:

The famous problem of V.A. Steklov is intimately related with the following
extremal problem. Fix degree and find a maximum of the orthonormal
polynomial with respect to measure from the Steklov class (i.e. class of probability measures
on the unit circle, such that its density is bounded away from zero at every Lebesgue point. We study
asymptotics of certain trigonometric polynomials defined by the Fejer convolutions. These polynomials can be used to construct asymptotical solutions of the above extremal problem.

Keywords:

Steklov problem; orthogonal polynomials on the circle; Fejer convolution.

Publication language:english,
pages:19

Research direction:

Mathematical problems and theory of numerical methods