Positivity

, Volume 22, Issue 1, pp 91–103 | Cite as

Unitarily invariant strictly positive definite kernels on spheres

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Abstract

We present a Fourier characterization for the continuous and unitarily invariant strictly positive definite kernels on the unit sphere in \({\mathbb {C}}^{q}\), thus adding to a celebrated work of I. J. Schoenberg on positive definite functions on real spheres.

Keywords

Positive definite Spheres Disk polynomials Zernike polynomials Unitary group 

Mathematics Subject Classification

42A82 42C10 43A35 

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.ICMC-USP - São CarlosSão CarlosBrazil

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