Multivariate positive definite functions on spheres
Metric Geometry
2014-09-17 v2 Combinatorics
Abstract
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.
Cite
@article{arxiv.math/0701083,
title = {Multivariate positive definite functions on spheres},
author = {Oleg R. Musin},
journal= {arXiv preprint arXiv:math/0701083},
year = {2014}
}
Comments
17 pages