Positive Definite Kernels on Complex Spheres

Abstract

AbstractContinuous 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