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Biorthogonal Rational Functions and the Generalized Eigenvalue Problem

✍ Scribed by Alexei Zhedanov

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 170 KB
Volume: 101
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1999.3339

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✦ Synopsis

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.

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