Biorthogonal rational functions and the generalized eigenvalue problem

JOURNAL OF APPROXIMATION THEORY

卷:101

Article

Zhedanov, A

关键词: biorthogonal rational functions;    generalized eigenvalue problem;    Christoffel Darboux formula;    spectral transformations;   

DOI  :  10.1006/jath.1999.3339

来源: Elsevier

【 摘 要 】

We present some general results concerning so-called biorthogonal polynomials of R-II type introduced by M. Ismail and D. Masson. These polynomials give rise to a pair of rational functions which are biorthogonal with respect to a linear functional, It is shown that these rational functions naturally appear as eigenvectors of the generalized eigenvalue problem for two arbitrary tri-diagonal matrices. We study spectral transformations of these functions leading to a rational modification of the linear functional. An analogue of the Christoffel-Darboux formula is obtained. (C) 1999 Academic Press.

【 授权许可】

Free