Asymptotic upper bounds for the entropy of orthogonal polynomials in the Szegő class

B. Beckermann, A. Martinez-Finkelshtein, E. A. Rakhmanov +1

We give an asymptotic upper bound as $n\to \infty$ for the entropy integral $$E_n(w)=-\int p_n^2(x)\log (p_n^2(x))w(x)dx,$$ where $p_n$ is the $n$th degree orthonormal polynomial w…