4 papers · 1 filter
Positive Cubature Compression and Optimal Hyperinterpolation Stability on a Conic Surface
Congpei An, Yan Ge
We study the computational cost and stability of positive cubature and hyperinterpolation on a truncated conic surface with a Jacobi-type weight. A classical quadratic disk-to-cone…
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…