摘要
证明了如果A是一有界强连续群的生成元,B是与A可交换的有界算子,且p(r)是一多项式,则在适当条件下,Bp(A)是一C半群(或积分半群)的生成元.并且将这种抽象结果应用到一些基本函数空间中的微分算子中去,得到了包括Kellermann和Hieber的一个重要结果在内的一些有趣结果.
Suppose A generates a bounded strongly continuous group, B is a bounded linear operator such that it commutes with A and that ‖eit‖ ≤M(1 + |t |n) (t∈R) . If p(r) is a polynomial such that ω=sup{Rep(ir);r∈R}<∞ and {‖exp(tRep(ir)B)‖;r∈R}≤Meat(t≥0) for some a∈R, then Bp(A) generates a C-semigroup S(t), which is continuous in operator-norm and satisfies ‖S(t)‖≤M(1 +tn+1)eat(t≥0) , where C=(ω' -p(A))-n-1 for some ω' >ω. If,in addition, σ(B) {λ6C;Reλ>0}, then Bp(A) generates an (n + 1)-times integrated semigroup T(t), which is continuous in operator-norm and satisfies ‖T(t)‖≤M(1 +tn+1)ebt(t≥0) , where b = max{0,a}. In application, a Kellermann and Hieber's result and other interesting results have been obtained.
出处
《华中理工大学学报》
CSCD
北大核心
1993年第5期171-175,共5页
Journal of Huazhong University of Science and Technology
基金
国家自然科学基金资助项目
关键词
强连续强
C半群
生成元
多项式
Strongly continuous group
C-semigroup
integrated semigroup
functional calculus
differential operator
