International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 12, Pages 715-724
Strict positive definiteness on spheres via disk polynomials
1Departamento de Matemática, ICMC-USP - São Carlos, Caixa Postal 668, São Carlos 13560-970, SP, Brazil
2Departamento de Matemática, CCE - Universidade Estadual de Maringá, Avenida Colombo 5790, Maringá 87020-900, PR, Brazil
Received 16 August 2001; Revised 3 April 2002
Copyright © 2002 V. A. Menegatto and A. P. Peron. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We characterize complex strictly positive definite functions on
spheres in two cases, the unit sphere of , , and the unit sphere of the complex . 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.