Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published October 2010 | Submitted
Journal Article Open

The Nevai Condition

Abstract

We study Nevai's condition that for orthogonal polynomials on the real line, K_n(x, x_0)^2K_n(x_0, x_0) ^(−1) dρ(x) → δ_(x0), where K_n is the Christoffel–Darboux 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.

Additional Information

© 2009 Springer Science+Business Media, LLC. Received: 4 September 2008. Accepted: 2 March 2009. Published online: 16 May 2009. We would like to thank David Damanik and Svetlana Jitomirskaya for valuable correspondence and Benjamin Weiss for valuable discussions. J.B. and B.S. would like to thank Ehud de Shalit for the hospitality of The Hebrew University where some of this work was done. Y.L. would like to thank Matthias Flach for the hospitality of Caltech where some of this work was done.

Attached Files

Submitted - 0809.2255

Files

Files (381.9 kB)
Name Size Download all
md5:758e7bd7ba65343a15e8ce3ebc76b444
381.9 kB Download

Additional details

Created:
August 22, 2023
Modified:
October 20, 2023