Multivariate positive definite functions on spheres

Details Multivariate positive definite functions on spheres Multivariate positive definite functions on spheres

2007-01-03

arxiv.org/abs/math/0701083v2

Mathematics

Metric Geometry

17 pages

Scientific paper

In 1942 I. J. Schoenberg proved that a function is positive definite in the unit sphere if and only if this function is a positive linear combination of the Gegenbauer polynomials. In this paper we extend Schoenberg's theorem for multivariate Gegenbauer polynomials. This extension derives new positive semidefinite constraints for the distance distribution which can be applied for spherical codes.

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