71 citations · 71 across the 7 of their papers we have counts for
6 papers · 1 filter
On Bernstein inequalities on the unit ball
Tomasz Beberok, Yuan Xu
Two types of Bernstein inequalities are established on the unit ball in , which are stronger than those known in the literature. The first type consists of inequaliti…
Approximation and orthogonality on fully symmetric domains
Yuan Xu
We study orthogonal polynomials on a fully symmetric planar domain that is generated by a certain triangle in the first quadrant. For a family of weight functions on , we sh…
Minimal cubature rules and Koornwinder polynomials
Yuan Xu
In his classical paper [5], Koornwinder studied a family of orthogonal polynomials of two variables, derived from symmetric polynomials. This family possesses a rare property that…
Highly localized kernels on space of homogeneous type
Yuan Xu
Highly localized kernels based on orthogonal polynomials have been studied and utilized over several regular domains. Much of the results deduced via these kernels can be treated u…
Orthogonal polynomials on domains of revolution
Yuan Xu
We study orthogonal polynomials for a weight function defined over a domain of revolution, where the domain is formed from rotating a two-dimensional region and goes beyond the qua…
Orthogonal polynomials of several variables
Yuan Xu
Preliminary version of Chapter 2 in the book "Encyclopedia of Special functions: The Askey-Bateman Project, Vol. 2: Multivariate special functions", T. H. Koornwinder and J. V. Sto…