Positive definite kernels on complex spheres

Abstract

Continuous bizonal positive definite kernels on the spheres in Cq are shown to be a series of disk polynomials with nonnegative coefficients. These kernels are the complex analogs of the so-called positive definite functions on real spheres introduced and characterized by I. J. Schoenberg (1942, Duke Math. J.9, 96-108). The result adds to the classes of functions from which one can generate radial basis function interpolants to arbitrary data on spheres. © 2001 Academic Press.