Construction of a parametrix for the Cauchy problem of some weakly hyperbolic equation III
Construction of a parametrix for the Cauchy problem of some weakly hyperbolic equation III
\S 0. Introduction Let (0. 0) P=P\{t, x , D_{t} , D_{x} ) =D_{t}^{2} -t^{2} \sum_{f,k=1}^{n}a_{jk}(t, x)D_{j}D_{k}+ +b_{0}(t, x)D_{t}+ \sum_{j=1}^{n}b_{j}(t, x)D_{j}+c(t, x) .Here a_{jk}(t, x) , b_{l}(t, x) , c(t, x) are C^{\infty} functions of (t, x)=(t, x_{1^{ }},\cdots, x_{n})\in R\cross \cross R^{n} , and D_{t}=-i\partial/\partial t , D_{f}=-i\partial/\partial x_{f} …