%0 Journal Article
%T Pseudodifferential multi-product representation of the solution operator of a parabolic equation
%A Hiroshi Isozaki
%A J¨¦r£¿me Le Rousseau
%J Mathematics
%D 2008
%I arXiv
%R 10.1080/03605300903017330
%X 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.
%U http://arxiv.org/abs/0801.3838v2