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.

翻译：论文对紧凑的里曼尼方形的绝对肯定的内核进行了研究。我们提出了新的条件,以确保一般内核和内核与某些革命结构的严格肯定性。我们还说明了产品内核在产品内核上的条件。作为两点同质空间产品的条件的例子,我们介绍了这些内核和内核在产品内核上的条件。