Journal article
Authors list: Buhmann, Martin; Jaeger, Janin
Publication year: 2020
Journal: Journal of Approximation Theory
Volume number: 257
ISSN: 0021-9045
eISSN: 1096-0430
Open access status: Bronze
DOI Link: https://doi.org/10.1016/j.jat.2020.105440
Publisher: Elsevier
Abstract:
Identifying (conditionally) strictly positive definite functions is of great importance as they allow the unique solution of certain interpolation problems. We introduce new sufficient (and some necessary) conditions for functions to be conditionally strictly positive definite on all spheres Sd-1, d > 2, only employing monotonicity properties. For strictly positive definite and conditionally negative definite functions on all spheres we give a characterisation in terms of monotonicity properties. Further, we prove that multiply monotone functions are positive definite on spheres up to a certain dimension. (C) 2020 Elsevier Inc. All rights reserved.
Citation Styles
Harvard Citation style: Buhmann, M. and Jaeger, J. (2020) Polya-type criteria for conditional strict positive definiteness of functions on spheres, Journal of Approximation Theory, 257, Article 105440. https://doi.org/10.1016/j.jat.2020.105440
APA Citation style: Buhmann, M., & Jaeger, J. (2020). Polya-type criteria for conditional strict positive definiteness of functions on spheres. Journal of Approximation Theory. 257, Article 105440. https://doi.org/10.1016/j.jat.2020.105440
Keywords
Completely monotone functions; Conditionally positive definite kernels; Dot product kernels; Interpolation of scattered data; Isotropic kernels; MULTIPLY MONOTONE-FUNCTIONS; SCATTERED DATA; Spherical basis functions
