Asymptotic zero distribution for a class of multiple orthogonal polynomials
Classical Analysis and ODEs
2007-05-23 v1 Spectral Theory
Abstract
We establish the asymptotic zero distribution for polynomials generated by a four-term recurrence relation with varying recurrence coefficients having a particular limiting behavior. The proof is based on ratio asymptotics for these polynomials. We can apply this result to three examples of multiple orthogonal polynomials, in particular Jacobi-Pineiro, Laguerre I and the example associated with Macdonald functions. We also discuss an application to Toeplitz matrices.
Cite
@article{arxiv.math/0606440,
title = {Asymptotic zero distribution for a class of multiple orthogonal polynomials},
author = {E. Coussement and J. Coussement and W. Van Assche},
journal= {arXiv preprint arXiv:math/0606440},
year = {2007}
}
Comments
18 pages, 2 figures