H. Castro, M. et al., Laplace-Beltrami differentiability of positive definite kernels on the sphere, Acta mathematica Sinica. English series (Print) , 29(1), 2013, pp. 93-104
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.