A New Approach to Universality at the Edge of the Spectrum
Classical Analysis and ODEs
2007-05-23 v1
Abstract
We show how localization and smoothing techniques can be used to establish universality at the edge of the spectrum for a fixed positive measure on [-1,1]. Assume that the measure is a regular measure, and is absolutely continuous in some closed neighborhood J of 1. Assume that in J, w = h * Jacobi, where h(1)>0 and h is continuous at 1. Then universality at 1 for ourgiven measure follows from universality at 1 for the classical Jacobi weight. Note that no smoothness is required of h, only continuity.
Cite
@article{arxiv.math/0701169,
title = {A New Approach to Universality at the Edge of the Spectrum},
author = {Doron S Lubinsky},
journal= {arXiv preprint arXiv:math/0701169},
year = {2007}
}