The paper introduces a new characterization of strict positive definiteness for kernels on the 2-sphere without assuming the kernel to be radially (isotropic) or axially symmetric. The results use the series expansion of the kernel in spherical harmonics. Then additional sufficient conditions are proven for kernels with a block structure of expansion coefficients. These generalize the result derived by Chen et al. (2003, A necessary and sufficient condition for strictly positive definite functions on spheres. Proc. Amer. Math. Soc., 131, 2733–2740) for radial kernels to nonradial kernels.

中文翻译：

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2 球面上的严格正定核：从径向对称到特征值块结构

本文介绍了 2 球上核的严格正定性的新表征，而不假设核是径向（各向同性）或轴对称的。结果使用球谐函数中核的级数展开。然后证明了具有扩展系数块结构的核的附加充分条件。这些概括了陈等人得出的结果。(2003, 球面上严格正定函数的充分必要条件。Proc. Amer. Math. Soc., 131, 2733–2740) 用于径向核到非径向核。