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: | urn:nbn:de:hbz:386-kluedo-5424 |
| Series (Serial Number): | Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (141) |
| Document Type: | Preprint |
| Language of publication: | English |
| Year of Completion: | 1995 |
| Year of first Publication: | 1995 |
| Publishing Institution: | Technische Universität Kaiserslautern |
| Date of the Publication (Server): | 2000/06/07 |
| Faculties / Organisational entities: | Kaiserslautern - Fachbereich Mathematik |
| DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
| Licence (German): |  Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |