标题： 关于哈密顿量具有同心$δ$壳层的密集点谱和绝对连续谱 显示英文标题

标题： On the dense point and absolutely continuous spectrum for Hamiltonians with concentric $δ$ shells

摘要： 我们研究了在维度$d\ge 2$中带有奇异相互作用的薛定谔算子，该相互作用由一族无穷多个同心球面支撑，类似于 Hempel 和其合作者针对正则势所研究的系统。 本质谱覆盖了一个由适当的单维比较算子决定的半直线；在后者的间隙中它为密集纯点谱。如果相互作用是径向周期的，则存在绝对连续谱带；与正则情况相比，在高能极限下，点谱段的测度并不趋于零。 显示英文摘要

摘要： We consider Schr\"odinger operator in dimension $d\ge 2$ with a singular interaction supported by an infinite family of concentric spheres, analogous to a system studied by Hempel and coauthors for regular potentials. The essential spectrum covers a halfline determined by the appropriate one-dimensional comparison operator; it is dense pure point in the gaps of the latter. If the interaction is radially periodic, there are absolutely continuous bands; in contrast to the regular case the measure of the p.p. segments does not vanish in the high-energy limit.