## On a New Condition for Strictly Positive Definite Functions on Spheres

• 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 ofXu and Cheney.

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Author: Michael Schreiner urn:nbn:de:hbz:386-kluedo-5424 Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (141) Preprint English 1995 1995 Technische Universität Kaiserslautern 2000/06/07 Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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