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| HAL: hal-00202495, version 1 |
| arXiv: 0801.0941 |
| DOI: 10.1007/s00041-008-9057-6 |
| Detailed view |  Export this paper |
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| Journal of fourier analysis and applications 15 (2009) 561-582 |
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| On the extremal rays of the cone of positive, positive definite functions |
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| Philippe Jaming 1Maté Matolcsi 2 |
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| (2009) |
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| The aim of this paper is to investigate the cone of non-negative, radial, positive-definite functions in the set of continuous functions on $\R^d$. Elements of this cone admit a Choquet integral representation in terms of the extremals. The main feature of this article is to characterize some large classes of such extremals. In particular, we show that there many other extremals than the gaussians, thus disproving a conjecture of G. Choquet and that no reasonable conjecture can be made on the full set of extremals. The last feature of this article is to show that many characterizations of positive definite functions available in the literature are actually particular cases of the Choquet integral representations we obtain. |
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| 1: | Mathématiques et Applications, Physique Mathématique d'Orléans (MAPMO) |
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CNRS : UMR6628 – Université d'Orléans |
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| 2: | Renyi Institute |
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Renyi Institute |
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| Subject | : | Mathematics/Classical Analysis and ODEs Mathematics/Functional Analysis Mathematics/Probability |
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| Choquet integral representation – extremal ray generators – positive definite functions |
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| hal-00202495, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00202495 | |
| oai:hal.archives-ouvertes.fr:hal-00202495 | |
| From: Philippe Jaming | |
| Submitted on: Monday, 7 January 2008 11:34:04 | |
| Updated on: Thursday, 8 October 2009 15:29:14 | |
