Convex linear combinations of sequences of monic orthogonal polynomials
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- by A. Cachafeiro and F. Marcellan PDF
- Proc. Amer. Math. Soc. 126 (1998), 2323-2331 Request permission
Abstract:
For a sequence $\{\Phi _n\}_0^\infty$ of monic orthogonal polynomials (SMOP), with respect to a positive measure supported on the unit circle, we obtain necessary and sufficient conditions on a SMOP $\{Q_n\}_0^\infty$ in order that a convex linear combination $\{R_n\}_0^\infty$ with $R_n=\beta \Phi _n+(1-\beta )Q_n$ be a SMOP with respect to a positive measure supported on the unit circle.References
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Additional Information
- A. Cachafeiro
- Affiliation: Departamento de Matemática Aplicada, E.T.S.I.I., Universidad de Vigo, Spain
- Email: acachafe@dma.uvigo.es
- F. Marcellan
- Affiliation: Departamento de Matemáticas, E.P.S., Universidad Carlos III de Madrid, Spain
- Email: pacomarc@ing.uc3m.es
- Received by editor(s): March 4, 1996
- Received by editor(s) in revised form: January 13, 1997
- Additional Notes: The work of the first author was supported by the DGICYT under grant number PB93-1169.
The work of the second author was supported by an Acción Integrada Hispano-Austriaca 4B/1995. - Communicated by: J. Marshall Ash
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2323-2331
- MSC (1991): Primary 42C05
- DOI: https://doi.org/10.1090/S0002-9939-98-04272-5
- MathSciNet review: 1443374