科研之友
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摘要
We show that isotropic positive definite functions on the d-dimensional sphere which are 2k times differentiable at zero have 2k + [(d - 1)/2] continuous derivatives on (0, pi). This result is analogous to the result for radial positive definite functions on Euclidean spaces. We prove optimality of the result for all odd dimensions. The proof relies on montee, descente and turning bands operators on spheres which parallel the corresponding operators originating in the work of Matheron for radial positive definite functions on Euclidean spaces.
- 出版日期2017-7
