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This article is cited in 8 scientific papers (total in 8 papers)
Positive Definite Functions on Complex Spheres and their Walks through Dimensions
Eugenio Massaa, Ana Paula Perona, Emilio Porcubc a Departamento de Matemática, ICMC-USP – São Carlos, Caixa Postal 668, 13560-970 São Carlos SP, Brazil
b Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, 230123, Chile
c School of Mathematics and Statistics, Chair of Spatial Analytics Methods,
University of Newcastle, UK
Abstract:
We provide walks through dimensions for isotropic positive definite functions defined over complex spheres. We show that the analogues of Montée and Descente operators as proposed by Beatson and zu Castell [J. Approx. Theory 221 (2017), 22–37] on the basis of the original Matheron operator [Les variables régionalisées et leur estimation, Masson, Paris, 1965], allow for similar walks through dimensions. We show that the Montée operators also preserve, up to a constant, strict positive definiteness. For the Descente operators, we show that strict positive definiteness is preserved under some additional conditions, but we provide counterexamples showing that this is not true in general. We also provide a list of parametric families of (strictly) positive definite functions over complex spheres, which are important for several applications.
Keywords:
Descente; disk polynomials; Montée; positive definite functions.
Received: April 6, 2017; in final form October 30, 2017; Published online November 8, 2017
Citation:
Eugenio Massa, Ana Paula Peron, Emilio Porcu, “Positive Definite Functions on Complex Spheres and their Walks through Dimensions”, SIGMA, 13 (2017), 088, 16 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1288 https://www.mathnet.ru/eng/sigma/v13/p88
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