On discrete orthogonal polynomials of several variables

2004/01/29 by Yuan Xu, Xu, Yuan · 1 citation
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical functions and polynomials #Matrix Theory and Algorithms #math.CA

paper · pdf · doi:10.48550/arxiv.math/0401418

15 pages, 2 figures

openalex publication_date 2004/01/29 · arxiv created 2004/04/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let V be a set of isolated points in \RR^d. Define a linear functional \CL on the space of real polynomials restricted on V, \CL f = ∑_{x ∈ V} f(x)ρ(x), where ρ is a nonzero function on V. Polynomial subspaces that contain discrete orthogonal polynomials with respect to the bilinear form = \CL(f g) are identified. One result shows that the discrete orthogonal polynomials still satisfy a three-term relation and Favard's theorem holds in this general setting.

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