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arXiv · 1503.04786

Darboux transformations for multivariate orthogonal polynomials

Gerardo Ariznabarreta·Manuel Mañas
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Abstract

Darboux transformations for polynomial perturbations of a real multivariate measure are found. The 1D Christoffel formula is extended to the multidimensional realm: multivariate orthogonal polynomials are expressed in terms of last quasi-determinants and sample matrices. The coefficients of these matrices are the original orthogonal polynomials evaluated at a set of nodes, which is supposed to be poised. A discussion for the existence of poised sets is given in terms of algebraic hypersufaces in the complex affine space.

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Gerardo Ariznabarreta, Manuel Mañas. 2015-03-16. Darboux transformations for multivariate orthogonal polynomials. https://doi.org/10.1016/j.jat.2017.10.007

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