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) |
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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: |
05 Dec 2022 14:34 |
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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