AN EXTENSION OF A THEOREM OF SCHOENBERG TO PRODUCTS OF SPHERES
By J. Guella, Valdir Antonio Menegatto, A. Peron. 2015
47 citations recorded by the source corpus.
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 I. J. Schoenberg on positive definiteness on a single sphere. We also discuss a few issues regarding the characterization, including topics for future investigation.
Subfields: Applied Mathematics, Computational Mechanics
View Paper: https://www.semanticscholar.org/paper/364330b031de2efae8f0199b933ae8fc217f94d0
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In Applied Mathematics
Citations in the corpus
- From Schoenberg Coefficients to Schoenberg Functions (2015, background): “tinuous positive definite functions on Sd × TN is given in [25, 4 Theorem 3.1]. This result corresponds to our result, when the locally compact group G is the N-dimensional torus TN. In a recent paper [15] Guella, Menegatto and Peron consider isotropic kernels K((ξ,ζ),(η,χ) = f(ξ ·η,ζ ·χ), ξ,η ∈ Sd, ”