ASYMPTOTIC ALMOST PERIODICITY OF C-SEMIGROUPS
ASYMPTOTIC ALMOST PERIODICITY OF C-SEMIGROUPS
复制标题
C-半群的渐近近似周期性
DOI：
10.1155/s0161171203108034
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发表时间：
2003
影响因子：
1.2
通讯作者：
F. Huang
中科院分区：
文献类型：
--
作者：
Linghong Xie;Miao Li;F. Huang
本文讨论了C-半群的渐近概周期性。证明了若A生成一个渐近概周期C半群，则C的值域有类似的分解。这里我们使用的技巧是A的Hille-Yosida空间，它是X的极大嵌入子空间，使得A在这个子空间上的部分生成C 0半群。关键的事实是抽象柯西问题的温和解在Hille-Yosida空间中是渐近概周期的当且仅当它在X中是渐近概周期的，并且温和解在Hille-Yosida空间中在无穷远处为零当且仅当它在X中为零。在适当的谱条件下，得到了C-半群的渐近概周期性的一个更容易证明的定理（定理3.7）。
In this paper, we will discuss the asymptotic almost periodicity of C-semigroups. We show that if A generates an asymptotically almost periodic Csemigroup, then the range of C has an analogous decomposition. The technique we use here is the Hille-Yosida space for A, which is a maximal imbedded subspace of X such that the part of A on this subspace generates a C0semigroup. The crucial facts are that a mild solution of the abstract Cauchy problem is asymptotically almost periodic in the Hille-Yosida space if and only if it is asymptotically almost periodic in X, and the mild solution is vanishing at infinity in the Hille-Yosida space if and only if it is vanishing in X. Under suitable spectral conditions, we obtain a theorem for asymptotic almost periodicity of C-semigroups that is more easily testified (Theorem 3.7).