Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 10, Number 4 (2016), 671-685.
An extension of a theorem of Schoenberg to products of spheres
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.
Banach J. Math. Anal., Volume 10, Number 4 (2016), 671-685.
Received: 1 July 2015
Accepted: 19 December 2015
First available in Project Euclid: 31 August 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 43A35: Positive definite functions on groups, semigroups, etc.
Secondary: 33C50: Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable 33C55: Spherical harmonics 42A10: Trigonometric approximation 42A82: Positive definite functions
Guella, J. C.; Menegatto, V. A.; Peron, A. P. An extension of a theorem of Schoenberg to products of spheres. Banach J. Math. Anal. 10 (2016), no. 4, 671--685. doi:10.1215/17358787-3649260. https://projecteuclid.org/euclid.bjma/1472657851