English

The Nevai Condition

Spectral Theory 2008-09-15 v1 Mathematical Physics math.MP

Abstract

We study Nevai's condition that for orthogonal polynomials on the real line, Kn(x,x0)2Kn(x0,x0)1dρ(x)δx0K_n(x,x_0)^2 K_n(x_0,x_0)^{-1} d\rho (x)\to\delta_{x_0} where KnK_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][-2,2] where it fails on an interval.

Cite

@article{arxiv.0809.2255,
  title  = {The Nevai Condition},
  author = {Jonathan Breuer and Yoram Last and Barry Simon},
  journal= {arXiv preprint arXiv:0809.2255},
  year   = {2008}
}
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