On Discrete Orthogonal Polynomials of Several Variables
نویسنده
چکیده
Let V be a set of points in R. Define a linear functional L on the space of polynomials, Lf = ∑ x∈V f(x)ρ(x), where ρ is a nonzero function on V . The structure of discrete orthogonal polynomials of several variables with respect to the bilinear form 〈f, g〉 = L(fg) is studied. For a given V , the subspace of polynomials that will generate orthogonal polynomials on V is identified. One result shows that the orthogonal polynomials still satisfy a three-term relation and Favard’s theorem holds in this setting.
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