Derivatives of isotropic positive definite functions on spheres

Trübner, Mara; Ziegel, Johanna F. (2017). Derivatives of isotropic positive definite functions on spheres. Proceedings of the American Mathematical Society, 145(7), pp. 3017-3031. American Mathematical Society 10.1090/proc/13561

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We show that isotropic positive definite functions on the d -dimensional sphere which are 2k times differentiable at zero have 2k+[(d−1)/2] continuous derivatives on (0,π) . This result is analogous to the result for radial positive definite functions on Euclidean spaces. We prove optimality of the result for all odd dimensions. The proof relies on mont\'ee, descente and turning bands operators on spheres which parallel the corresponding operators originating in the work of Matheron for radial positive definite functions on Euclidian spaces.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Trübner, Mara and Ziegel, Johanna F.

Subjects:

300 Social sciences, sociology & anthropology > 360 Social problems & social services
500 Science > 510 Mathematics

ISSN:

0002-9939

Publisher:

American Mathematical Society

Language:

English

Submitter:

Johanna Fasciati-Ziegel

Date Deposited:

25 Apr 2017 17:42

Last Modified:

13 Mar 2021 14:19

Publisher DOI:

10.1090/proc/13561

BORIS DOI:

10.7892/boris.94729

URI:

https://boris.unibe.ch/id/eprint/94729

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