Strictly positive definite kernels on the $2$-sphere: beyond radial symmetry

Strictly positive definite non-isotropic kernels on two-point homogeneous manifolds: The asymptotic approach

We present sufficient condition for a family of positive definite kernels on a compact two-point homogeneous space to be strictly positive definite based on their representation as a series of spherical harmonics. The family analyzed is a generalization of the isotropic kernels and the case of a real sphere is analyzed in details.

Strictly positive definite kernels on compact Riemannian manifolds

The paper studies strictly positive definite kernels on compact Riemannian manifolds. We state new conditions to ensure strict positive definiteness for general kernels and kernels with certain convolutional structure. We also state conditions for such kernels on product manifolds. As an example conditions for products of two-point homogeneous spaces are presented.

正则域上的正定函数

Positive definite functions on a regular domain

本文在正则域（如单位球、锥面、双曲面等）上定义并研究正定与严格正定函数，利用保距映射嵌入单位球面象限，推导出这些函数的刻画条件。

Strict positive definiteness of convolutional and axially symmetric kernels on d-dimensional spheres

The paper introduces new sufficient conditions of strict positive definiteness for kernels on d-dimensional spheres which are not radially symmetric but possess specific coefficient structures. The results use the series expansion of the kernel in spherical harmonics. The kernels either have a convolutional form or are axially symmetric with respect to one axis. The given results on convolutional kernels generalise the result derived by Chen et al. [8] for radial kernels. Keywords: strictly positive definite kernels, covariance functions, sphere

Positive Definite Multi-Kernels for Scattered Data Interpolations

In this article, we use the knowledge of positive definite tensors to develop a concept of positive definite multi-kernels to construct the kernel-based interpolants of scattered data. By the techniques of reproducing kernel Banach spaces, the optimal recoveries and error analysis of the kernel-based interpolants are shown for a special class of strictly positive definite multi-kernels.

球面上核微分矩阵的谱稳定性与扰动结果

Spectral stability and perturbation results for kernel differentiation matrices on the sphere

本文研究球面上由配点生成的核微分矩阵的谱性质，给出全局矩阵的扰动估计并证明谱符号保持，进而推导局部RBF-FD矩阵的谱界，数值实验验证理论结果。