Applications of semigroups of operators to non-elliptic differential operators

This paper treats systematically the semigroup method of non-elliptic diffe rential operators, which was developed in the last ten years. In particular , a review of the applications of regularized semigroups to non-elliptic di fferential operators with constant coefficients or time-dependent coefficie nts, parabolic systems, correct systems, abstract differential operators an d pseudodifferential operators is given here. It is also shown that the reg ularized semigroup is an appropriate tool for non-elliptic differential ope rators and is far superior to the integrated semigroup approach.