|
Archivo Abierto Institucional de la Universidad Carlos III de Madrid >
Investigación >
Departamentos >
Departamento de Matemáticas >
Grupo de Análisis Matemático Aplicado (GAMA) >
DM - GAMA - Artículos de Revistas >
Please use this identifier to cite or link to this item:
http://hdl.handle.net/10016/5942
|
| Title: | Two variable orthogonal polynomials and structured matrices |
| Author(s): | Delgado, Antonia M.
Geronimo, Jeffrey S.
Iliev, Plamen
Marcellán, Francisco |
| Publisher: | Society for Industrial and Applied Mathematics (SIAM) |
| Issued date: | 2006 |
| Citation: | SIAM Journal on Matrix Analysis and Applications, 2006, vol. 28, n. 1, p. 118-147 |
| URI: | http://hdl.handle.net/10016/5942 |
| ISSN: | 0895-4798 (Print)
1095-7162 (Online) |
| DOI: | 10.1137/05062946X |
| Description: | 30 pages, no figures.-- MSC2000 codes: 42C05, 30E05, 47A57.
MR#: MR2218946 (2006m:47021)
Zbl#: Zbl 1136.42305 |
| Abstract: | We consider bivariate real valued polynomials orthogonal with respect to a positive linear functional. The lexicographical and reverse lexicographical orderings are used to order the monomials. Recurrence formulas are derived between polynomials of different degrees. These formulas link the orthogonal polynomials constructed using the lexicographical ordering with those constructed using the reverse lexicographical ordering. Relations between the coefficients in the recurrence formulas are established and used to give necessary and sufficient conditions for the existence of a positive linear functional. Links to the theory of matrix orthogonal polynomials are developed as well the consequences of a zero assumption on one of the coefficients in the the recurrence formulas. |
| Sponsor: | The second and fourth authors were partially supported by NATO grant PST.CLG.979738. The second author was partially supported by an NSF grant. The first and fourth authors were partially supported by grant BFM2003-06335-C03-02 from the Dirección General de Investigación, Ministerio de Educación y Ciencia of Spain. |
| Review: | PeerReviewed |
| Publisher version: | http://dx.doi.org/10.1137/05062946X |
| Keywords: | Bivariate orthogonal polynomials
Positive linear functionals
Moment problem
Hankel matrices |
| Rights: | © Society for Industrial and Applied Mathematics (SIAM) |
| Appears in Collections: | DM - GAMA - Artículos de Revistas
|
Items in E-Archivo are protected by copyright, with all rights reserved, unless otherwise indicated.
|
