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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Metadaten
Author:Michael Schreiner
URN (permanent link):urn:nbn:de:hbz:386-kluedo-5424
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (141)
Document Type:Preprint
Language of publication:English
Year of Completion:1995
Year of Publication:1995
Publishing Institute:Technische Universität Kaiserslautern
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik

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