Interlacing properties of zeros of multiple orthogonal polynomials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:389

Article

Haneczok, Maciej¹  Van Assche, Walter¹ 

[1] Katholieke Univ Leuven, Dept Math, BE-3001 Louvain, Belgium

关键词: Multiple orthogonal polynomials;    Recurrence relations;    Interlacing zeros;   

DOI  :  10.1016/j.jmaa.2011.11.077

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free