积分半群的Lumer-Phillips定理(英文)

The Lumer-Phillips Theorems for Integrated Semigroups

一个ｎ次积分半群Ｓ（ｔ）如果满足｜｜Ｓ（ｎ）ｘ｜｜≤｜｜ｘ｜｜， ｔ≥０，ｘ∈Ｄ（Ａｎ），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．在本文中，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．

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 n - times integrated semigronps and give the Lumer-Phillips theorem for n -times integrated semigronps.