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Banach空间上混合性C0半群的谱条件
Spectral Conditions of Mixing $C_0$}-semigroups on Banach Spaces

姚玉武,陈秀,朱玉扬,康素玲
YAO Yuwu*,CHEN Xiu,ZHU Yuyang,KANG Suling

合肥学院数学与物理系, 合肥, 安徽, 230601
Department of Mathematics & Physics, Hefei University, Hefei, Anhui, 230601, P. R. China

收稿日期: 2010-10-13
出版日期: 2013-06-25
DOI: 10.11845/sxjz.2010124b

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摘要 设$\{T(t): t\geq0\}$是Banach空间$X$上的一个$C_0$-半群, $A$表示它的无穷小生成子. 本文利用$A$的点谱给出了$C_0$-半群$\{T(t): t\geq0\}$是否为混合半群的充分条件. 同时利用权函数刻画了转移半群的混合性,并由此说明了所给的谱条件不是必要的.
关键词 $C_0$-半群混合性点谱转移半群    
Abstract:Let $\{T(t): t\geq 0\}$ be a $C_0$-semigroup onBanach space $X$ and $A$ denote its infinitesimalgenerator. Using the point spectrum of $A$, we give sufficient conditions for $\{T(t): t\geq 0\}$to be mixing or not mixing. We also characterize mixing by admissible weight function for thetranslation semigroup, and employing this characterization we show that the spectral condition for$\{T(t): t\geq 0\}$ to be mixing is not necessary.
Key wordsmixing    point spectrum    translation semigroup
基金资助:Science Foundation of Department ofEducation of Anhui Province(No. KJ2012Z340) and Foundation forExcellent Young Talents in College of Anhui Province(No.2010SQRL158)
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