Jonathan Breuer, Yoram Last, Barry Simon
The Nevai Condition
(377K, pdf)

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.