Positive-definite functions on spheres and Sidelnikov inequality
نویسندگان
چکیده
منابع مشابه
Multivariate positive definite functions on spheres
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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In this paper we study strictly positive definite functions on the unit sphere of the m-dimensional Euclidean space. Such functions can be used for solving a scattered data interpolation problem on spheres. Since positive definite functions on the sphere were already characterized by Schoenberg some fifty years ago, the issue here is to determine what kind of positive definite functions are act...
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ژورنال
عنوان ژورنال: Journal of Classical Analysis
سال: 2017
ISSN: 1848-5987
DOI: 10.7153/jca-2017-11-05