摘要
首先，本文利用Ｈｉｌｂｅｒｔ空间的特性推广了算子半群的Ｌａｐｌｃａｅ反演表示，其次。
In this paper, it is shown that if T(t)(t≥0) is a C 0 semigroup generated by operator A in Hilbert space, then for all t>0, σ> max {0,w(A)}, the following Laplace inversion formula is valid T(t)x= lim r→+∞12 π i∫ σ+ir σ-ir e -λt R(λ,A)x d λ, for all x∈H in which the limit is uniform on for all T>0. The other result is that if there exists ω>0 such that {λ: Re λ>ω}ρ(A) and sup α>ω∫ ∞ -∞ ‖(α+iτ-A) -1 x‖ 2 d τ<∞, for all x∈E then A generates an integrated semigroup S(t) (t≥0) satisfying ‖S(t)‖≤M e ωt (t≥0) (in which E is a Banach space).
出处
《工程数学学报》
CSCD
北大核心
1997年第1期15-20,共6页
Chinese Journal of Engineering Mathematics
基金
陕西省自然科学基金
