Geodesic
Multivariate Orthogonal Polynomials and Modified Moment Functionals
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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Multivariate orthogonal polynomials can be introduced by using a moment functional defined on the linear space of polynomials in several variables with real coefficients. We study the so-called Uvarov and Christoffel modifications obtained by adding to the moment functional a finite set of mass points, or by multiplying it times a polynomial of total degree $2$, respectively. Orthogonal polynomials associated with modified moment functionals will be studied, as well as the impact of the modification in useful properties of the orthogonal polynomials. Finally, some illustrative examples will be given.
Keywords: multivariate orthogonal polynomials; moment functionals; Christoffel modification; Uvarov modification; ball polynomials. 
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Antonia M. Delgado; Lidia Fernández; Teresa E. Pérez; Miguel A. Piñar. Multivariate Orthogonal Polynomials and Modified Moment Functionals. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a89/

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