Strictly positive definite kernels on a product of spheres

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• 作者：J.C. Guella ^{jeanguella@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; V.A. Menegatto ; ^{menegatt@icmc.usp.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Positive definite kernels ; Strictly positive definite ; Isotropy ; Product of spheres ; Schoenberg theorem ; Gegenbauer polynomials
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 March 2016
• 年：2016
• 卷：435
• 期：1
• 页码：286-301
• 全文大小：387 K

文摘

For the real, continuous, isotropic and positive definite kernels on a product of spheres, one may consider not only its usual strict positive definiteness but also strict positive definiteness restrict to the points of the product that have distinct components. In this paper, we provide a characterization for strict positive definiteness in these two cases, settling all the cases but those in which one of the spheres is a circle.