2007/01/05 by D. S. Lubinsky, Doron S Lubinsky, Lubinsky, Doron S
Mathematics · #41 #42 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Random Matrices and Applications #Spectral Theory in Mathematical Physics #math.CA #msc:41 #msc:42
paper · pdf · doi:10.48550/arxiv.math/0701169
arxiv created 2007/01/05 · openalex publication_date 2007/01/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.