5 papers
Optimal differentiability of isotropic positive definite functions on even-dimensional spheres
Yan Ge
We prove optimality of the differentiability bound for isotropic positive definite functions on every even-dimensional sphere. If the even continuation of such a function on the $d…
Isotropic Positive Definite Functions on Spheres: Even-Dimensional Gneiting's Problem
Yan Ge
We study when a compactly supported isotropic positive definite function on a Euclidean space remains positive definite after Euclidean distance is replaced by spherical geodesic d…
Isotropic Positive Definite Functions on Spheres
Han Feng, Yan Ge
In this paper, we investigate the relationship between positive definite functions on the unit sphere $\sph$ and on the Euclidean space $\RR^d$. For the dimension to be odd, a…
Best approximation by polynomials on the conic domains
Yan Ge, Yuan Xu
A new modulus of smoothness and its equivalent -function are defined on the conic domains in , and used to characterize the weighted best approximation by polynomi…
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…