Generalized Convolution Roots of Positive Definite Kernels on Complex   Spheres
  Convolution is an important tool in the construction of positive definite kernels on a manifold. This contribution provides conditions on an $L^2$-positive definite and zonal kernel on the unit sphere of $\mathbb{C}^q$ in order that the kernel can be recovered as a generalized convolution root of an equally positive definite and zonal kernel. 
Victor S. Barbosa and Valdir A. Menegatto
math.CA math.FA