The paper surveys interactions between complex and functional-analytic methods in the CauchyKovalevskaya theory. For instance, the behaviour of the derivative of a bounded holomorphic function led to abstract versions...The paper surveys interactions between complex and functional-analytic methods in the CauchyKovalevskaya 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.展开更多
A boundedness criterion is set up for some convolution operators on a compact Lie group.By this criterion a Hormander multiplier theorem is proved in the Hardy spaces on SU(2).
文摘The paper surveys interactions between complex and functional-analytic methods in the CauchyKovalevskaya 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.
文摘A boundedness criterion is set up for some convolution operators on a compact Lie group.By this criterion a Hormander multiplier theorem is proved in the Hardy spaces on SU(2).
