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A class of orthogonal functions given by a three term recurrence formula


Authors: C. F. Bracciali, J. H. McCabe, T. E. Pérez and A. Sri Ranga
Journal: Math. Comp. 85 (2016), 1837-1859
MSC (2010): Primary 42C05, 33C47; Secondary 65D32, 41A05, 33C45
DOI: https://doi.org/10.1090/mcom3041
Published electronically: September 21, 2015
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Abstract: We present a class of functions satisfying a certain orthogonality property for which there also exists a three term recurrence formula. This class of functions, which can be considered as an extension to the class of symmetric orthogonal polynomials on $ [-1,1]$, has a complete connection to the orthogonal polynomials on the unit circle. Interpolatory properties, quadrature rules and other properties based on the zeros of these functions are also considered.


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Additional Information

C. F. Bracciali
Affiliation: Departamento de Matemática Aplicada, IBILCE, UNESP - Universidade Estadual Paulista, 15054-000, São José do Rio Preto, SP, Brazil
Email: cleonice@ibilce.unesp.br

J. H. McCabe
Affiliation: Department of Applied Mathematics, School of Mathematics, University of St. Andrews, Scotland
Email: jhm@st-and.ac.uk

T. E. Pérez
Affiliation: Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain
Email: tperez@ugr.es

A. Sri Ranga
Affiliation: Departamento de Matemática Aplicada, IBILCE, UNESP - Universidade Estadual Paulista, 15054-000, São José do Rio Preto, SP, Brazil
Email: ranga@ibilce.unesp.br

DOI: https://doi.org/10.1090/mcom3041
Keywords: Orthogonal functions, self-inversive polynomials, three term recurrence, quadrature rules, orthogonal polynomials on the unit circle
Received by editor(s): January 10, 2014
Received by editor(s) in revised form: January 26, 2015
Published electronically: September 21, 2015
Additional Notes: This work was initiated during the exchange program CAPES(Brazil)/DGU(Spain) of 2008-2012
For this research the first and the fourth authors have also received support from CNPq (Grant no. 475502/2013-2) and FAPESP (Grant no. 2009/13832-9) of Brazil
The third author’s research was also supported by grants from Micinn of Spain and Junta de Andalucía.
Article copyright: © Copyright 2015 American Mathematical Society