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

中文翻译：

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d维球面上的卷积核和轴对称核的严格正定性

本文为d维球体上的核的正正定性引入了新的充分条件，这些维不是径向对称的，而是具有特定的系数结构。结果使用核在球谐函数中的级数展开。核具有卷积形式或相对于一个轴轴向对称。卷积核的给定结果推广了Chen等人得出的结果。[8]对于径向核。关键词：严格正定核，协方差函数，球体