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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Generators of rational spectral transformations for nontrivial $ \mathcal{C}$-functions


Authors: Kenier Castillo and Francisco Marcellán
Journal: Math. Comp. 82 (2013), 1057-1068
MSC (2010): Primary 42C05
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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Additional Information

Kenier Castillo
Affiliation: Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III, Leganés-Madrid, Spain
Email: kcastill@math.uc3m.es

Francisco Marcellán
Affiliation: Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III, Leganés-Madrid, Spain
Email: pacomarc@ing.uc3m.es

DOI: http://dx.doi.org/10.1090/S0025-5718-2012-02655-X
PII: S 0025-5718(2012)02655-X
Received by editor(s): August 31, 2011
Published electronically: November 28, 2012
Additional Notes: The work of the authors was supported by Dirección General de Investigación, Ministerio de Ciencia e Innovación of Spain, grant MTM2009-12740-C03-01.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.