On discrete orthogonal polynomials of several variables

Details On discrete orthogonal polynomials of several variables On discrete orthogonal polynomials of several variables

2004-01-29

arxiv.org/abs/math/0401418v2

Mathematics

Classical Analysis and ODEs

15 pages, 2 figures

Scientific paper

Let $V$ be a set of isolated points in $\RR^d$. Define a linear functional $\CL$ on the space of real polynomials restricted on $V$, $\CL f = \sum_{x \in V} f(x)\rho(x)$, where $\rho$ 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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