2021-07-29T03:43:24Zhttps://tsukuba.repo.nii.ac.jp/oaioai:tsukuba.repo.nii.ac.jp:000200032021-03-02T08:26:11ZPseudodifferential Multi-Product Representation of the Solution Operator of a Parabolic Equation磯崎, 洋Isozaki, HiroshiROUSSEAU, JÉRÔME LEBy using a time slicing procedure, we represent the solution operator of a second-order parabolic pseudodifferential equation on Ropfn 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.journal articleTaylor & Francis Group2009-07application/pdfCommunications in partial differential equations7346256550360-5302AA00611644https://tsukuba.repo.nii.ac.jp/record/20003/files/CPDE_34-7.pdfeng10.1080/03605300903017330© Taylor & Francis GroupThis is an electronic version of an article published in Hiroshi Isozaki,Jerome Le Rousseau \nPseudodifferential Multi-Product Representation of the Solution Operator of a Parabolic Equation\nCommunications in Partial Differential Equations, Volume 34, Issue 7 July 2009 pages 625 - 655.\nCommunications in Partial Differential Equations is available online at:http://www.informaworld.com/smpp/content~db=all?content=10.1080/03605300903017330