Open Access
October 2016 An extension of a theorem of Schoenberg to products of spheres
J. C. Guella, V. A. Menegatto, A. P. Peron
Banach J. Math. Anal. 10(4): 671-685 (October 2016). DOI: 10.1215/17358787-3649260


We present a characterization for the continuous, isotropic, and positive definite kernels on a product of spheres along the lines of a classical result of Schoenberg on positive definiteness on a single sphere. We also discuss a few issues regarding the characterization, including topics for future investigation.


Download Citation

J. C. Guella. V. A. Menegatto. A. P. Peron. "An extension of a theorem of Schoenberg to products of spheres." Banach J. Math. Anal. 10 (4) 671 - 685, October 2016.


Received: 1 July 2015; Accepted: 19 December 2015; Published: October 2016
First available in Project Euclid: 31 August 2016

zbMATH: 1348.43008
MathSciNet: MR3543906
Digital Object Identifier: 10.1215/17358787-3649260

Primary: 43A35
Secondary: 33C50 , 33C55 , 42A10 , 42A82

Keywords: addition formula , Gegenbauer polynomials , isotropy , positive definiteness , Spherical harmonics

Rights: Copyright © 2016 Tusi Mathematical Research Group

Vol.10 • No. 4 • October 2016
Back to Top