Multivariate Orthogonal Polynomials and Modified Moment Functionals

Symmetry Integrability and Geometry-Methods and Applications

article

Antonia M. Delgado¹  Lidia Fernández¹  Teresa E. Pérez¹  Miguel A. Piñar¹ 

[1] IEMath - Math Institute and Department of Applied Mathematics, University of Granada

关键词: multivariate orthogonal polynomials;    moment functionals;    Christof fel modification;    Uvarov modification;    ball polynomials;   

DOI  :  10.3842/SIGMA.2016.090

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown