Strictly and non-strictly positive definite functions on spheres
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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...
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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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Let H be any complex inner product space with inner product < ·, · >. We say that f : | C → | C is Hermitian positive definite on H if the matrix ( f(< z,z >) )n r,s=1 (∗) is Hermitian positive definite for all choice of z, . . . ,z in H, all n. It is strictly Hermitian positive definite if the matrix (∗) is also non-singular for any choice of distinct z, . . . ,z in H. In this article we prove...
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Strictly positive definite functions are used as basis functions for approximation methods in various contexts. Using a group theoretic interpretation of Bochner’s Theorem we give a sufficient condition for strictly positive definite functions on a semi-direct product which are invariant under the natural action of a given subgroup. As an application strictly positive definite, reflection invar...
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.
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ژورنال
عنوان ژورنال: Bernoulli
سال: 2013
ISSN: 1350-7265
DOI: 10.3150/12-bejsp06