论文标题
不连续性导致必需频谱
Discontinuities cause essential spectrum
论文作者
论文摘要
我们研究了与分段单调间隔转换相关的转移操作员，并表明每当Banach空间界限$ l^\ infty $，并且转换未能是马尔可夫，则基本频谱很大。建造一个Banach空间家族我们表明，基本光谱半径上的下限是最佳的。确实，这些Banach空间实现了与理论最佳可能情况所需的基本光谱半径。
We study transfer operators associated to piecewise monotone interval transformations and show that the essential spectrum is large whenever the Banach space bounds $L^\infty$ and the transformation fails to be Markov. Constructing a family of Banach spaces we show that the lower bound on the essential spectral radius is optimal. Indeed, these Banach spaces realise an essential spectral radius as close as desired to the theoretical best possible case.
