Cauchy problem for exponentially correct differential operators (Q1072701)

The differential operator \(P(D_ t,D_ x)\), \(t\in R\), \(x\in R^ n\) is called exponentially correct if for any \(\xi \in R^ n\) there exists such \(c=c(\xi)\) that \(P(\tau,\eta)\neq 0\) if Im\(\eta=\xi\), Im \(\tau<c\). This notion is applicable also to the operators \(P(t,x,D_ t,D_ x)\) with variable coefficients. The author indicates the function spaces in which the Cauchy problem for the equation \(Pu=f\) is well posed.