周期mild解和算子半群的谱(英)

Periodic Mild Solutions and the Spectrum of Operator Semigroups

设Ｘ是Ｈｉｌｂｅｒｔ空间，ｅ~Ａｔ是Ｘ上的（１，Ａ）类半群．本文给出了用（λ－Ａ）~－１的性质来描述ｅ~Ａｔ谱的特征，同时也得到了Ｂａｎａｃｈ空间Ｘ中使（１，Ａ）类半群谱映射定理成立的一些充分条件．

Let X be a Hilbert space, e^At be a (1,A)-semigroup on X. In this paper we give characterizations of the spectrum of e^At in terms of properties of (λ-A) ^-1. On Banach space X, we establish some sufficient conditions on which the spectrum mapping theorem of (1,A)-semigroups holds.