| Abstract: | The paper surveys interactions between complex and functional-analytic methods in the Cauchy-Kovalevskaya theory. For instance, the behaviour of the derivative of a bounded holomorphic function led to abstract versions of the Cauchy-Kovalevskaya Theorem.Recent trends in the Cauchy-Kovalevskaya theory are based on the concept of associated differential operators. Since an evolution operator may posses several associated operators, initial data may be decomposed into components belonging to different associated spaces. This technique makes it also possible to solve ill-posed initial value problems. |
