On a new condition for strictly positive definite functions on spheres
نویسندگان
چکیده
منابع مشابه
Strictly Positive Definite Functions on Spheres
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...
متن کاملA Necessary and Sufficient Condition for Strictly Positive Definite Functions on Spheres
We give a necessary and sufficient condition for the strict positivedefiniteness of real and continuous functions on spheres of dimension greater than one.
متن کاملStrictly positive definite functions on spheres in Euclidean spaces
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...
متن کاملOn a New Condition for Strictly Positive De nite Functions on Spheres
Recently, Xu and Cheney (1992) have proved that if all the Legendre coeecients of a zonal function deened on a sphere are positive then the function is strictly positive deenite. It will be shown in this paper, that even if nitely many of the Legendre coeecients are zero, the strict positive deeniteness can be assured. The results are based on approximation properties of singular integrals, and...
متن کاملMultivariate 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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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1997
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-97-03634-4