Positive Definite Functions on Complex Spheres and their Walks through Dimensions
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 vari...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2017 |
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| Sprache: | Englisch |
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Інститут математики НАН України
2017
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149263 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862578261681242112 |
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| author | Massa, E. Peron, A.P. Porcu, E. |
| author_facet | Massa, E. Peron, A.P. Porcu, E. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-11-26T16:39:41Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149263 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T16:39:41Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Massa, E. Peron, A.P. Porcu, E. 2019-02-19T19:31:13Z 2019-02-19T19:31:13Z 2017 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 https://nasplib.isofts.kiev.ua/handle/123456789/149263 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. The authors gratefully thank the anonymous referees for the constructive comments and recommendations which helped to greatly improve the paper. Eugenio Massa was supported by
 grant #2014/25398-0, S˜ao Paulo Research Foundation (FAPESP) and grant #308354/2014-1,
 CNPq/Brazil. Ana P. Peron was supported by grants #2016/03015-7 and #2014/25796-5, S˜ao
 Paulo Research Foundation (FAPESP). Emilio Porcu was supported by grant FONDECYT
 #1170290 from the Chilean government. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Positive Definite Functions on Complex Spheres and their Walks through Dimensions Article published earlier |
| spellingShingle | Positive Definite Functions on Complex Spheres and their Walks through Dimensions Massa, E. Peron, A.P. Porcu, E. |
| title | Positive Definite Functions on Complex Spheres and their Walks through Dimensions |
| title_full | Positive Definite Functions on Complex Spheres and their Walks through Dimensions |
| title_fullStr | Positive Definite Functions on Complex Spheres and their Walks through Dimensions |
| title_full_unstemmed | Positive Definite Functions on Complex Spheres and their Walks through Dimensions |
| title_short | Positive Definite Functions on Complex Spheres and their Walks through Dimensions |
| title_sort | positive definite functions on complex spheres and their walks through dimensions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149263 |
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