Below is the ascii version of the abstract for 08-165. The html version should be ready soon.

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.