Szegő and para-orthogonal polynomials on the real line: Zeros and canonical spectral transformations
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- by Kenier Castillo, Regina Litz Lamblém, Fernando Rodrigo Rafaeli and Alagacone Sri Ranga PDF
- Math. Comp. 81 (2012), 2229-2249 Request permission
Abstract:
We study polynomials which satisfy the same recurrence relation as the Szegő polynomials, however, with the restriction that the (reflection) coefficients in the recurrence are larger than one in modulus. Para-orthogonal polynomials that follow from these Szegő polynomials are also considered. With positive values for the reflection coefficients, zeros of the Szegő polynomials, para-orthogonal polynomials and associated quadrature rules are also studied. Finally, again with positive values for the reflection coefficients, interlacing properties of the Szegő polynomials and polynomials arising from canonical spectral transformations are obtained.References
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Additional Information
- Kenier Castillo
- Affiliation: Departamento de Ciências de Computação e Estatística, IBILCE, Universidade Estadual Paulista - UNESP, Brazil
- Address at time of publication: Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III, Leganés-Madrid, Spain
- MR Author ID: 924654
- Email: kcastill@math.uc3m.es
- Regina Litz Lamblém
- Affiliation: Universidade Estadual de Mato Grosso do Sul - UEMS, Brazil
- Email: lamblem@uems.br
- Fernando Rodrigo Rafaeli
- Affiliation: Departamento de Matemática, Estatística e Computação, FCT, Universidade Estadual Paulista - UNESP, Brazil
- Email: rafaeli@fct.unesp.br
- Alagacone Sri Ranga
- Affiliation: Departamento de Ciências de Computação e Estatística, IBILCE, Universidade Estadual Paulista - UNESP, Brazil
- MR Author ID: 238837
- Email: ranga@ibilce.unesp.br
- Received by editor(s): April 20, 2011
- Received by editor(s) in revised form: June 12, 2011, and July 19, 2011
- Published electronically: April 2, 2012
- Additional Notes: This work has been done in the framework of a joint project of Dirección General de Investigación, Ministerio de Educación Ciencia of Spain and the Brazilian Science Foundation CAPES, Project CAPES/DGU 160/08.
The work of the first author was supported by Dirección General de Investigación, Ministerio de Ciencia e Innovación of Spain, grant MTM2009-12740-C03-01.
The work of the second, third and fourth authors was supported by FAPESP under grant 2009/13832-9.
The work of the fourth author was supported by CNPq. - © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 81 (2012), 2229-2249
- MSC (2010): Primary 42C05, 30B70; Secondary 30E05
- DOI: https://doi.org/10.1090/S0025-5718-2012-02593-2
- MathSciNet review: 2945153