Publication:
Two variable orthogonal polynomials and structured matrices

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ISSN: 0895-4798 (Print)
ISSN: 1095-7162 (Online)
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2006
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Society for Industrial and Applied Mathematics (SIAM)
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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.
Description
30 pages, no figures.-- MSC2000 codes: 42C05, 30E05, 47A57.
MR#: MR2218946 (2006m:47021)
Zbl#: Zbl 1136.42305
Keywords
Bivariate orthogonal polynomials, Positive linear functionals, Moment problem, Hankel matrices
Bibliographic citation
SIAM Journal on Matrix Analysis and Applications, 2006, vol. 28, n. 1, p. 118-147