Strict positive definiteness on spheres via disk polynomials
V. A. Menegatto1and A. P. Peron2
Received16 Aug 2001
Revised03 Apr 2002
Abstract
We characterize complex strictly positive definite functions on
spheres in two cases, the unit sphere of ℂq, q≥3, and the unit sphere of the complex ℓ2. The results depend upon
the Fourier-like expansion of the functions in terms of disk
polynomials and, among other things, they enlarge the classes of
strictly positive definite functions on real spheres studied in
many recent papers.