论文标题
带有嵌入特征值的准官方域
Quasi-conical domains with embedded eigenvalues
论文作者
论文摘要
任何准式开放式套装上的dirichlet laplacian的频谱与非阴性半轴相吻合。我们表明，有一个连接的准官方开放集，使得相应的dirichlet laplacian具有阳性（嵌入式）特征值。该开放式套件被构造为尺寸不断增长的立方体塔，该尺寸通过消失的尺寸连接。此外，我们表明可以选择该构造中的窗户的大小，以使Dirichlet Laplacian的绝对连续光谱是空的。
The spectrum of the Dirichlet Laplacian on any quasi-conical open set coincides with the non-negative semi-axis. We show that there is a connected quasi-conical open set such that the respective Dirichlet Laplacian has a positive (embedded) eigenvalue. This open set is constructed as the tower of cubes of growing size connected by windows of vanishing size. Moreover, we show that the sizes of the windows in this construction can be chosen so that the absolutely continuous spectrum of the Dirichlet Laplacian is empty.
