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A semiclassical perspective on multivariate orthogonal polynomials

M. Alvarez de Morales·L. Fernández·T. E. Pérez·M. A. Piñar
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Abstract

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 analogous of the semiclassical Pearson differential equation, the structure relation and a differential--difference equation.

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M. Alvarez de Morales, L. Fernández, T. E. Pérez, M. A. Piñar. 2006-10-04. A semiclassical perspective on multivariate orthogonal polynomials. https://arxiv.org/abs/math/0610153

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