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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A necessary and sufficient condition for strictly positive definite functions on spheres


Authors: Debao Chen, Valdir A. Menegatto and Xingping Sun
Journal: Proc. Amer. Math. Soc. 131 (2003), 2733-2740
MSC (2000): Primary 41A05, 42A15; Secondary 33C45, 33C55
Published electronically: April 7, 2003
MathSciNet review: 1974330
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Abstract | References | Similar Articles | Additional Information

Abstract: We give a necessary and sufficient condition for the strict positive-definiteness of real and continuous functions on spheres of dimension greater than one.


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Additional Information

Debao Chen
Affiliation: Department of Computer Sciences, Oklahoma State University-Tulsa, Tulsa, Oklahoma 74106
Email: cdebao@cs.okstate.edu

Valdir A. Menegatto
Affiliation: ICMC-Universidade de Sao Paulo, Caixa Postal 668, 13560-970 Sao Carlos SP, Brasil
Email: menegatt@icmc.usp.br

Xingping Sun
Affiliation: Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804
Email: xis280f@smsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06730-3
PII: S 0002-9939(03)06730-3
Keywords: Strict positive-definiteness, spherical harmonics, Gegenbauer polynomials
Received by editor(s): March 16, 2001
Received by editor(s) in revised form: January 29, 2002
Published electronically: April 7, 2003
Communicated by: Andreas Seeger
Article copyright: © Copyright 2003 American Mathematical Society