Interlacing properties of zeros of multiple orthogonal polynomials
Classical Analysis and ODEs
2013-10-04 v1
Abstract
It is well known that the zeros of orthogonal polynomials interlace. In this paper we study the case of multiple orthogonal polynomials. We recall known results and some recursion relations for multiple orthogonal polynomials. Our main result gives a sufficient condition, based on the coefficients in the recurrence relations, for the interlacing of the zeros of neighboring multiple orthogonal polynomials. We give several examples illustrating our result.
Keywords
Cite
@article{arxiv.1108.3917,
title = {Interlacing properties of zeros of multiple orthogonal polynomials},
author = {Maciej Haneczok and Walter Van Assche},
journal= {arXiv preprint arXiv:1108.3917},
year = {2013}
}
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18 pages