A Christoffel-Darboux formula for multiple orthogonal polynomials
Classical Analysis and ODEs
2010-07-29 v1 Complex Variables
Abstract
Bleher and Kuijlaars recently showed that the eigenvalue correlations from matrix ensembles with external source can be expressed by means of a kernel built out of special multiple orthogonal polynomials. We derive a Christoffel-Darboux formula for this kernel for general multiple orthogonal polynomials. In addition, we show that the formula can be written in terms of the solution of the Riemann-Hilbert problem for multiple orthogonal polynomials, which will be useful for asymptotic analysis.
Cite
@article{arxiv.math/0402031,
title = {A Christoffel-Darboux formula for multiple orthogonal polynomials},
author = {E. Daems and A. B. J. Kuijlaars},
journal= {arXiv preprint arXiv:math/0402031},
year = {2010}
}
Comments
11 pages, no figures