The Nevai Condition

Abstract

We study Nevai's condition that for orthogonal polynomials on the real line, $K_n(x,x_0{)}^2{K}_n(x_0,x_0{)}^{-1}d\rho (x)\to {\delta }_{x_0}$ where $K_n$ is the CD kernel. We prove that it holds for the Nevai class of a finite gap set uniformly on the spectrum and we provide an example of a regular measure on $[-2,2]$ where it fails on an interval.

References in corpus (1)

• Bulk Universality and Clock Spacing of Zeros for Ergodic Jacobi Matrices with A.C. Spectrum