Universality limits for generalized Jacobi measures

2016/05/13 by Tivadar Danka, Danka, Tivadar
Mathematics · Physics and Astronomy · #31A99 #33C10 #33C45 #42C05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.CA #math.MP #msc:31A99 #msc:33C10 #msc:33C45 #msc:42C05

paper · pdf · doi:10.48550/arxiv.1605.04275

55 pages

arxiv created 2016/05/13 · arxiv updated 2016/05/16

Abstract

In this paper universality limits are studied in connection with measures which exhibit power-type singular behavior somewhere in their support. We extend the results of Lubinsky for Jacobi measures supported on [-1,1] to generalized Jacobi measures supported on a compact subset of the real line, where the singularity can be located in the interior or at an endpoint of the support. The analysis is based upon the Riemann-Hilbert method, Christoffel functions, the polynomial inverse image method of Totik and the normal family approach of Lubinsky.

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