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Multivariate Orthogonal Polynomials and Modified Moment Functionals

Authors
  • Delgado, Antonia M.
  • Fernández, Lidia
  • Pérez, Teresa E.
  • Piñar, Miguel A.
Type
Preprint
Publication Date
Jan 26, 2016
Submission Date
Jan 26, 2016
Identifiers
arXiv ID: 1601.07194
Source
arXiv
License
Yellow
External links

Abstract

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.

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