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Positive Definite Kernels on Complex Spheres

✍ Scribed by V.A Menegatto; A.P Peron

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 111 KB
Volume: 254
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2000.7264

No coin nor oath required. For personal study only.

✦ Synopsis

Continuous bizonal positive definite kernels on the spheres in ‫ރ‬ q are shown to be a series of disk polynomials with nonnegative coefficients. These kernels are the complex analogs of the so-called positive definite functions on real spheres intro-Ž . duced and characterized by I. J. Schoenberg 1942, Duke Math. J. 9, 96᎐108 . The result adds to the classes of functions from which one can generate radial basis function interpolants to arbitrary data on spheres.

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