This contribution gives results on the action of the Laplace-Beltrami derivative on suffi- ciently smooth kernels on the sphere, those defined by absolutely and uniformly expansions generated by a family of at least c...This contribution gives results on the action of the Laplace-Beltrami derivative on suffi- ciently 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.展开更多
基金supported by CAPES-Brasilsupported by FAPESP-Brasil(Grant No.2010/19734-6)
文摘This contribution gives results on the action of the Laplace-Beltrami derivative on suffi- ciently 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.
