On asymptotic behavior of Heine-Stieltjes and Van Vleck polynomials
Classical Analysis and ODEs
2009-03-17 v1 Mathematical Physics
Complex Variables
math.MP
Abstract
We investigate the strong asymptotics of Heine-Stieltjes polynomials - polynomial solutions of a second order differential equations with complex polynomial coefficients. The solution is given in terms of critical measures (saddle points of the weighted logarithmic energy on the plane), that are tightly related to quadratic differentials with closed trajectories on the plane. The paper is a continuation of the research initiated in [arXiv:0902.0193]. However, the starting point here is the WKB method, which allows to obtain the strong asymptotics.
Keywords
Cite
@article{arxiv.0903.2614,
title = {On asymptotic behavior of Heine-Stieltjes and Van Vleck polynomials},
author = {A. Martinez-Finkelshtein and E. A. Rakhmanov},
journal= {arXiv preprint arXiv:0903.2614},
year = {2009}
}
Comments
24 pages, 6 figures