ON EXPONENTIAL STABILITY OF C-0 SEMIGROUPS

In this note, the exponential stability for C-0 semigroups in a Hilber t space is considered. First, an expression for a C-0 semigroup is giv en, and then a formula on the growth order of a C-0 semigroup is obtai ned. Finally, with some additional condition such as the boundedness o f the resolvent of the generator of a C-0 semigroup on an imaginary ad s, the exponential stability of a C-0 semigroup is proved. (C) 1998 Ac ademic Press.