Strictly Positive Definite Kernels on a Product of Spheres II - Guella, J.C.; Menegatto, V.A.; Peron, A.P. (Symmetry, Integrability and Geometry: Methods and Applications, 2016)
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].