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Pré-Publication, Document De Travail Année : 2007

Pseudodifferential multi-product representation of the solution operator of a parabolic equation

Hiroshi Isozaki
  • Fonction : Auteur
  • PersonId : 846305
Jérôme Le Rousseau
  • Fonction : Auteur
  • PersonId : 2249
  • IdHAL : jlr
  • IdRef : 155029207

Résumé

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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Dates et versions

hal-00216207 , version 1 (24-01-2008)
hal-00216207 , version 2 (17-04-2009)

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Hiroshi Isozaki, Jérôme Le Rousseau. Pseudodifferential multi-product representation of the solution operator of a parabolic equation. 2007. ⟨hal-00216207v1⟩
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