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

Author(s): Debao Chen; Valdir A. Menegatto; Xingping Sun
Journal: Proc. Amer. Math. Soc. 131 (2003), 2733-2740.
MSC (2000): Primary 41A05, 42A15; Secondary 33C45, 33C55
Posted: April 7, 2003
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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: 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
Posted: April 7, 2003
Communicated by: Andreas Seeger
Copyright of article: Copyright 2003, American Mathematical Society

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