RT Journal Article
T1 Two variable orthogonal polynomials and structured matrices
A1 Delgado, Antonia M.
A1 Geronimo, Jeffrey S.
A1 Iliev, Plamen
A1 Marcellán Español, Francisco José
AB 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.
PB Society for Industrial and Applied Mathematics (SIAM)
SN 0895-4798 (Print)
SN 1095-7162 (Online)
YR 2006
FD 2006
LK https://hdl.handle.net/10016/5942
UL https://hdl.handle.net/10016/5942
LA eng
NO 30 pages, no figures.-- MSC2000 codes: 42C05, 30E05, 47A57.
NO MR#: MR2218946 (2006m:47021)
NO Zbl#: Zbl 1136.42305
NO 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.
DS e-Archivo
RD 20 jun. 2024