Generators of rational spectral transformations for nontrivial 𝒞-functions

Castillo, Kenier; Marcellán, Francisco

doi:10.1090/S0025-5718-2012-02655-X

Generators of rational spectral transformations for nontrivial $\mathcal {C}$-functions
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by Kenier Castillo and Francisco Marcellán;

Math. Comp. 82 (2013), 1057-1068

DOI: https://doi.org/10.1090/S0025-5718-2012-02655-X

Published electronically: November 28, 2012

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Abstract:

In this paper we consider transformations of sequences of orthogonal polynomials associated with a Hermitian linear functional $\mathcal {L}$ using spectral transformations of the corresponding $\mathcal {C}$-function $F_{\mathcal {L}}$. We show that a rational spectral transformation of $F_{\mathcal {L}}$ with polynomial coefficients is a finite composition of four canonical spectral transformations.

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