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| HAL : hal-00216207, version 2 |
| arXiv : 0801.3838 |
| DOI : 10.1080/03605300903017330 |
| Fiche détaillée |  Récupérer au format |
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| Comm. Partial Differential Equations 34, 7 (2009) 625 - 655 |
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| Versions disponibles : | v1 (24-01-2008) | v2 (17-04-2009) |
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| Pseudodifferential multi-product representation of the solution operator of a parabolic equation |
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| Hiroshi Isozaki 1Jérôme Le Rousseau 2, 3 |
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| (2009) |
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| By using a time slicing procedure, we represent the solution operator of a second-order parabolic pseudodifferential equation on $\R^n$ as an infinite product of zero-order pseudodifferential operators. A similar representation formula is proven for parabolic differential equations on a compact Riemannian manifold. Each operator in the multi-product is given by a simple explicit Ansatz. The proof is based on an effective use of the Weyl calculus and the Fefferman-Phong inequality. |
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| 1 : | Institute of Mathematics |
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University of Tsukuba |
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| 2 : | Laboratoire d'Analyse, Topologie, Probabilités (LATP) |
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CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III |
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| 3 : | Mathématiques et Applications, Physique Mathématique d'Orléans (MAPMO) |
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CNRS : UMR6628 – Université d'Orléans |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Parabolic equation – Pseudodifferential initial value problem – Weyl quantization – Infinite product of operators – Compact manifold |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00216207, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00216207/fr/ | |
| oai:hal.archives-ouvertes.fr:hal-00216207_v2 | |
| Contributeur : Jérôme Le Rousseau | |
| Soumis le : Vendredi 17 Avril 2009, 14:33:52 | |
| Dernière modification le : Lundi 14 Septembre 2009, 19:07:57 | |
