Laplace-Beltrami differentiability of positive definite kernels on the sphere |
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Authors: | M H Castro V A Menegatto C P Oliveira |
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Abstract: | This contribution gives results on the action of the Laplace-Beltrami derivative on sufficiently smooth kernels on the sphere, those defined by absolutely and uniformly expansions generated by a family of at least continuous functions. Among other things, the results show that convenient Laplace-Beltrami derivatives of positive definite kernels on the sphere are positive definite too. We also include similar results on the action of the Laplace-Beltrami derivative on condensed spherical harmonic expansions. |
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Keywords: | Sphere Laplace-Beltrami operator Laplace-Beltrami derivative positive definite kernels spherical harmonics |
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