Positive Definite Functions on Complex Spheres and their Walks through Dimensions
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Positive Definite Functions on Complex Spheres and their Walks through Dimensions
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| Creator |
Massa, E.
Peron, A.P. Porcu, E. |
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| Description |
We provide walks through dimensions for isotropic positive definite functions defined over complex spheres. We show that the analogues of Montée and Descente operators as proposed by Beatson and zu Castell [J. Approx. Theory 221 (2017), 22-37] on the basis of the original Matheron operator [Les variables régionalisées et leur estimation, Masson, Paris, 1965], allow for similar walks through dimensions. We show that the Montée operators also preserve, up to a constant, strict positive definiteness. For the Descente operators, we show that strict positive definiteness is preserved under some additional conditions, but we provide counterexamples showing that this is not true in general. We also provide a list of parametric families of (strictly) positive definite functions over complex spheres, which are important for several applications.
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| Date |
2019-02-19T19:31:13Z
2019-02-19T19:31:13Z 2017 |
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| Type |
Article
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| Identifier |
Positive Definite Functions on Complex Spheres and their Walks through Dimensions / E. Massa, A.P. Peron, E. Porcu // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 49 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 42A82; 42C10; 42C05; 30E10; 62M30 DOI:10.3842/SIGMA.2017.088 http://dspace.nbuv.gov.ua/handle/123456789/149263 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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