arXiv subjects

Clotilde Martínez

Publications and source records attributed to Clotilde Martínez.

2 recordsLinked to original sources

arXiv2017

Asymptotic behaviour of the Christoffel functions on the Unit Ball in the presence of a Mass on the Sphere

We present a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes a mass uniformly distributed on the sphere. First, connection formulas relating these multivariate orthogonal polynomials and the classical ball polynomials are obtained. Then, using the representation formula for these polynomials in terms of spherical harmonics analytic properties will be deduced. Finally, we analyze the asymptotic behaviour of the Christoffel functions.

math.CA↗

arXiv2016

Orthogonal Polynomials on the Unit Ball and Fourth-Order Partial Differential Equations

The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere. First, we will get connection formulas relating classical multivariate orthogonal polynomials on the ball with our family of orthogonal polynomials. Then, using the representation of these polynomials in terms of spherical harmonics, algebraic and differential properties will be deduced.

math.CA↗