Pseudodifferential Multi-Product Representation of the Solution Operator of a Parabolic Equation |
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Authors: | Hiroshi Isozaki |
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Institution: | Institute of Mathematics, University of Tsukuba , Tsukuba, Japan |
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Abstract: | By using a time slicing procedure, we represent the solution operator of a second-order parabolic pseudodifferential equation on ? 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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Keywords: | Compact manifold Infinite product of operators Parabolic equation Pseudodifferential initial value problem Weyl quantization |
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