Pseudodifferential multi-product representation of the solution operator   of a parabolic equation
  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. 
Hiroshi Isozaki, J\'er\^ome Le Rousseau (LATP, MAPMO)