Strictly Positive Definite Kernels on a Product of Spheres II
Classical Analysis and ODEs
2016-10-31 v2
Abstract
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
Cite
@article{arxiv.1605.09775,
title = {Strictly Positive Definite Kernels on a Product of Spheres II},
author = {Jean C. Guella and Valdir A. Menegatto and Ana P. Peron},
journal= {arXiv preprint arXiv:1605.09775},
year = {2016}
}