Convolution roots and differentiability of isotropic positive definite functions on spheres

Johanna Ziegel

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arXiv · 1201.5833

Convolution roots and differentiability of isotropic positive definite functions on spheres

Johanna Ziegel

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Abstract

We prove that any isotropic positive definite function on the sphere can be written as the spherical self-convolution of an isotropic real-valued function. It is known that isotropic positive definite functions on d-dimensional Euclidean space admit a continuous derivative of order [(d-1)/2]. We show that the same holds true for isotropic positive definite functions on spheres and prove that this result is optimal for all odd dimensions.

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Johanna Ziegel. 2013-10-28. Convolution roots and differentiability of isotropic positive definite functions on spheres. https://arxiv.org/abs/1201.5833

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