Pseudodifferential Multi-Product Representation of the Solution Operator of a Parabolic Equation
Pseudodifferential Multi-Product Representation of the Solution Operator of a Parabolic Equation
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DOI：
10.1080/03605300903017330
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发表时间：
2008-01
影响因子：
1.9
通讯作者：
H. Isozaki;Jérôme Le Rousseau
中科院分区：
文献类型：
--
作者：
H. Isozaki;Jérôme Le Rousseau
利用时间切片方法，我们将ℝn上一类二阶抛物型拟微分方程解算子表示为零级拟微分算子的无穷乘积。证明了紧致黎曼流形上抛物型方程的一个类似的表示式。乘积中的每个运算符都由一个简单的显式Anatz给出。证明是基于Weyl微积分和Fefferman-Phong不等式的有效使用。
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.