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Convex linear combinations of sequences
of monic orthogonal polynomials

Authors: A. Cachafeiro and F. Marcellan
Journal: Proc. Amer. Math. Soc. 126 (1998), 2323-2331
MSC (1991): Primary 42C05
MathSciNet review: 1443374
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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.

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Additional Information

A. Cachafeiro
Affiliation: Departamento de Matemática Aplicada, E.T.S.I.I., Universidad de Vigo, Spain

F. Marcellan
Affiliation: Departamento de Matemáticas, E.P.S., Universidad Carlos III de Madrid, Spain

Keywords: Orthogonal polynomials, C-functions, measures on the unit circle
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
Article copyright: © Copyright 1998 American Mathematical Society