Trübner, Mara; Ziegel, Johanna F. (2017). Derivatives of isotropic positive definite functions on spheres. Proceedings of the American Mathematical Society, 145(7), pp. 30173031. 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: 
00029939 
Publisher: 
American Mathematical Society 
Language: 
English 
Submitter: 
Johanna FasciatiZiegel 
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 