On the size of the polynomials orthonormal on the unit circle with respect to a measure which is a sum of the Lebesgue measure and 𝑃 point masses

Abstract

For the measures on the unit circle that are equal to the sum of Lebesgue measure and p p point masses, we give an estimate on the size of the corresponding orthonormal polynomials. As a simple corollary of the method, we obtain a bound for some exponential polynomials.