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Proceedings of the American Mathematical Society
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Proceedings of the American Mathematical Society
Article . 2003 . Peer-reviewed
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A necessary and sufficient condition for strictly positive definite functions on spheres

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 07 Apr 2003 English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society, volume 131, pages 2,733-2,740 (issn: 0002-9939, eissn: 1088-6826, Copyright policy )
Authors: Chen, Debao; Menegatto, Valdir A.; Sun, Xingping;

doi: 10.1090/s0002-9939-03-06730-3

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

Abstract

In this paper a necessary and sufficient condition for the strict positive-definiteness of real and continuous functions on spheres of dimension greater than one is given.

Related Organizations
Keywords

Harmonic analysis on homogeneous spaces, Gegenbauer polynomials, strict positive-definiteness, Positive definite functions in one variable harmonic analysis, spherical harmonics, Positive definite functions on groups, semigroups, etc., Spherical harmonics

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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 77
    popularity
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    		 Top 10%
    influence
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    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
77
Top 10%
Top 10%
Top 10%
bronze