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Positive definite functions on complex spheres and their walks through dimensions

Lookup NU author(s): Professor Emilio Porcu

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Abstract

© 2017, Institute of Mathematics. All rights reserved. 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.

Publication metadata

Author(s): Massa E, Peron AP, Porcu E

Publication type: Article

Publication status: Published

Journal: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Year: 2017

Volume: 13

Online publication date: 08/11/2017

Acceptance date: 30/10/2017

ISSN (electronic): 1815-0659

Publisher: Institute of Mathematics

URL: https://doi.org/10.3842/SIGMA.2017.088

DOI: 10.3842/SIGMA.2017.088

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