On a New Condition for Strictly Positive De nite Functions on Spheres
نویسنده
چکیده
Recently, Xu and Cheney (1992) have proved that if all the Legendre coeecients of a zonal function deened on a sphere are positive then the function is strictly positive deenite. It will be shown in this paper, that even if nitely many of the Legendre coeecients are zero, the strict positive deeniteness can be assured. The results are based on approximation properties of singular integrals, and provide also a completely diierent proof of the results of Xu and Cheney.
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