Generalized convolution roots of positive definite kernels on complex spheres

Abstract

Convolution is an important tool in the construction of positive definite kernels on a manifold. This contribution provides conditions on an 'L POT.2'-positive definite and zonal kernel on the unit sphere of 'C POT.Q' in order that the kernel can be recovered as a generalized convolution root of an equally positive definite and zonal kernel.