A semiclassical perspective on multivariate orthogonal polynomials

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摘要

Differential properties for orthogonal polynomials in several variables are studied. We consider multivariate orthogonal polynomials whose gradients satisfy some quasi-orthogonality conditions. We obtain several characterizations for these polynomials including the analogues of the semiclassical Pearson differential equation, the structure relation and a differential-difference equation.

论文关键词：42C05,33C50,Orthogonal polynomials in several variables,Semiclassical orthogonal polynomials

论文评审过程：Received 28 September 2006, Revised 24 January 2007, Available online 14 March 2007.

论文官网地址：https://doi.org/10.1016/j.cam.2007.03.005