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

Abstract : 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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https://hal.archives-ouvertes.fr/hal-00216207
Contributor : Jérôme Le Rousseau <>
Submitted on : Friday, April 17, 2009 - 2:33:52 PM
Last modification on : Wednesday, October 10, 2018 - 1:26:33 AM
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Hiroshi Isozaki, Jérôme Le Rousseau. Pseudodifferential multi-product representation of the solution operator of a parabolic equation. Comm. Partial Differential Equations, 2009, 34 (7), pp.625 - 655. ⟨10.1080/03605300903017330⟩. ⟨hal-00216207v2⟩

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