有界可测函数的一致谱与Carleman谱的等价性
Equality of uniform and Carleman spectra for bounded measurable functions
摘要：
本文研究了$ϕ:\jj\to X$函数的各种类型的谱，其中$\jj\in\{\r_+,\r\}$和$X$是一个复巴拿赫空间。我们证明了[15]中定义的均匀谱与$ϕ\in L^{\infty}(\r,X)$的Carleman谱一致。该结果也适用于$ϕ\in L^{\infty}(\r_+,X)$的拉普拉斯（半线）谱。我们还指出了一类Laplace谱与Carleman谱相等的有界可测函数
英文摘要：
In this paper we study various types of spectra of functions $ϕ:\jj\to X$, where $\jj\in\{\r_+,\r\}$ and $X$ is a complex Banach space. We show that uniform spectrum defined in [15] coincides with Carleman spectrum for $ϕ\in L^{\infty}(\r,X)$. This result holds true also for Laplace (half-line) spectrum for $ϕ\in L^{\infty}(\r_+,X)$. We also indicate a class of bounded measurable functions for which Laplace spectrum and Carleman spectrum are equal
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