The global parametrix in the Riemann-Hilbert steepest descent analysis for orthogonal polynomials
Classical Analysis and ODEs
2011-04-05 v2 Mathematical Physics
math.MP
Abstract
In the application of the Deift-Zhou steepest descent method to the Riemann-Hilbert problem for orthogonal polynomials, a model Riemann-Hilbert problem that appears in the multi-cut case is solved with the use of hyperelliptic theta functions. We present here an alternative approach which uses meromorphic differentials instead of theta functions to construct the solution of the model Riemann-Hilbert problem.
Keywords
Cite
@article{arxiv.0909.5626,
title = {The global parametrix in the Riemann-Hilbert steepest descent analysis for orthogonal polynomials},
author = {Arno Kuijlaars and Man Yue Mo},
journal= {arXiv preprint arXiv:0909.5626},
year = {2011}
}
Comments
22 pages, 1 figure, to appear in Computational Methods and Function Theory