Banach空间积分双半群的生成条件(英文)

A Generation Condition of Integrated Bisemigroup on Banach Space

研究Banach空间中积分双半群的生成条件.利用算子A的豫解算子,给出了积分双半群T(t)的生成定理.结果表明:如果对任意的x∈X,f∈X*,以及A|λ]<δ,λ∈ρ(A),有<R(σ+i·;A)x,f>∈Lp(R),则存在算子族S(t),t∈R,S(t)强连续且满足积分双半群的定义.

The generation condition of integrated bisemigroup in Banach space is studied in this paper. Using the resolvent of operator A , a generation theorem of integrated bisemigroup T(t) is proved. The result is showed that if ν|λ| <δ, λ∈ ρ(A), and satisfy 〈R(σ+ i·; A)x, f〉 ∈Lp(R), for all x∈X, f∈X* , then there exists a family operators S(t), t∈R, which is strongly continuous and satisfies the definition of integrated bisemigroup.