Antonia M. Delgado, Lidia Fernández, Teresa E. Pérez, Miguel A. Piñar
Published 2016-01-26Version 1
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.
A semiclassical perspective on multivariate orthogonal polynomials
Asymptotics of multivariate orthogonal polynomials with hyperoctahedral symmetry
Asymptotic behaviour of the Christoffel functions on the Unit Ball in the presence of a Mass on the Sphere
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