On discrete orthogonal polynomials of several variables
Abstract
Description
Let $V$ be a set of isolated points in $\RR^d$. Define a linear functional $\CL$ on the space of real polynomials restricted on $V$, $\CL f = \sum_{x \in V} f(x)ρ(x)$, where $ρ$ is a nonzero function on $V$. Polynomial subspaces that contain discrete orthogonal polynomials with respect to the bilinear form $<f,g> = \CL(f g)$ 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.
15 pages, 2 figures
15 pages, 2 figures