Differentiable Positive Definite Kernels on Spheres
V. A. Menegatto, Claudemir Pinheiro de Oliveira, Ana Paula Perón · Journal of Applied Analysis · 2009
We analyze term-by-term differentiability of uniformly convergent series of the form , where S m –1 is the unit sphere in , and { Y k } is a sequence of spherical harmonics or even more general functions. Since this class of kernels includes the continuous positive definite kernels on S m –1 , the results in this paper will show that, under certain conditions, the action of convenient differential operators on positive definite (strictly positive definite) kernels on S m –1 generate positive definite kernels.