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On a new condition for strictly
positive definite functions on spheres

Author: Michael Schreiner
Journal: Proc. Amer. Math. Soc. 125 (1997), 531-539
MSC (1991): Primary 43A35, 43A90, 42A82, 41A05
MathSciNet review: 1353398
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Abstract: Recently, Xu and Cheney (1992) have proved that if all the Legendre coefficients of a zonal function defined on a sphere are positive then the function is strictly positive definite. It will be shown in this paper that, even if finitely many of the Legendre coefficients are zero, the strict positive definiteness can be assured. The results are based on approximation properties of singular integrals, and provide also a completely different proof of the results of Xu and Cheney.

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Additional Information

Michael Schreiner
Affiliation: University of Kaiserslautern, Laboratory of Technomathematics, Geomathematics Group, P.O. Box 30 49, 67653 Kaiserslautern, Germany

Keywords: Positive definite functions, spherical interpolation
Received by editor(s): August 29, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society