Convolution roots and differentiability of isotropic positive definite functions on spheres

Ziegel, Johanna F. (2014). Convolution roots and differentiability of isotropic positive definite functions on spheres. Proceedings of the American Mathematical Society, 142(6), pp. 2063-2077. American Mathematical Society 10.1090/S0002-9939-2014-11989-7

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We prove that any isotropic positive definite function on the sphere can be written as the spherical self-convolution of an isotropic real-valued function. It is known that isotropic positive definite functions on d-dimensional Euclidean space admit a continuous derivative of order [(d − 1)/2]. We show that the same holds true for isotropic positive definite functions on spheres and prove that this result is optimal for all odd dimensions.

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:

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:

Lutz Dümbgen

Date Deposited:

18 Jun 2014 10:52

Last Modified:

25 Apr 2017 23:48

Publisher DOI:

10.1090/S0002-9939-2014-11989-7

BORIS DOI:

10.7892/boris.53282

URI:

https://boris.unibe.ch/id/eprint/53282

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