Geodesic
Strictly Positive Definite Kernels on a Product of Spheres II
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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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].
Keywords: positive definite kernels; strictly positive definiteness; isotropy; covariance functions; sphere; circle. 
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Jean C. Guella; Valdir A. Menegatto; Ana P. Peron. Strictly Positive Definite Kernels on a Product of Spheres II. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a102/

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