45 citations · 194 across the 100 of their papers we have counts for
104 papers
Addition formula for two families of orthogonal polynomials in several variables
Yuan Xu
An addition formula is a closed-form formula for reproducing kernels of orthogonal polynomials of several variables; the latter are kernels of orthogonal projection operators. We d…
Orthogonal polynomials which are eigenfunctions of a partial differential operator
Yuan Xu
We study orthogonal polynomials of variables with respect to a wrapped product weight function for $(\…
Bernstein inequality on parabolic domains
Yuan Xu
Several families of sharp Bernstein inequalities are established on the weighted space over parabolic domains, which include bounded or unbounded rotational paraboloids and p…
Sharp Bernstein inequalities on simplex
Yan Ge, Yuan Xu
We prove several new families of Bernstein inequalities of two types on the simplex. The first type consists of inequalities in norm for the Jacobi weight, some of which are…
A Generalized Pell's equation for a class of multivariate orthogonal polynomials
Jean-Bernard Lasserre, Yuan Xu
We extend the polynomial Pell's equation satisfied by univariate Chebyshev polynomials on [--1, 1] from one variable to several variables, using orthogonal polynomials on regular d…
Continued fractions and orthogonal polynomials in several variables
Tomas Sauer, Yuan Xu
We extend the close interplay between continued fractions, orthogonal polynomials, and Gaussian quadrature rules to several variables in a special but natural setting which we char…