积分半群的Lumer—Phillips定理

一个n次积分半群S(t)如果满足‖S^(n)(t)x‖≤‖x‖，A↓t≥0,x∈D(A^n)，我们就称S(t)是一压缩的n次积分半群，其中A为半群S（t)的生成元。在本中，我们完全刻划了n次压缩积分半群的特征，给出了n次压缩积分半群的Lumer-Phillips定理。

The Lumer-PhillipsTheorems for Integrated Semigroups

An n-times integrated semigroup (S (t))t≥0 is of contractions if ‖ S(n) (t)x‖≤‖x‖for t≥0.x ∈ D(An).where A is the generator of S(t).We completely characterize the generators of contraction ntimes integrated semigroups and give the Lumer-Phillips theorem for n -times integrated semigroups.