Strictly Positive Definite Kernels on a Product of Spheres II

Strictly Positive Definite Kernels on a Product of Spheres II

We present, among other things, a necessary and sufficient condition for the strict positive definiteness of an isotropic and positive definite kernel on the cartesian product of a circle and a higher dimensional sphere. The result complements similar results previously obtained for strict positive...

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Veröffentlicht in:arXiv.org 2016-10
Hauptverfasser: Guella, Jean C, Menegatto, Valdir A, Peron, Ana P
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Kernel functions
Mathematics - Classical Analysis and ODEs
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description We present, among other things, a necessary and sufficient condition for the strict positive definiteness of an isotropic and positive definite kernel on the cartesian product of a circle and a higher dimensional sphere. The result complements similar results previously obtained for strict positive definiteness on a product of circles [Positivity, to appear, arXiv:1505.01169] and on a product of high dimensional spheres [J. Math. Anal. Appl. 435 (2016), 286-301, arXiv:1505.03695].
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Mathematics - Classical Analysis and ODEs
title Strictly Positive Definite Kernels on a Product of Spheres II
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