关于同心$δ$壳Hamilton算子的稠密点和绝对连续谱
On the dense point and absolutely continuous spectrum for Hamiltonians with concentric $δ$ shells
摘要：
我们考虑薛定谔算子在维度$d\ge 2$与奇异相互作用支持的一个无限的家庭的同心球，类似于一个系统的研究由亨佩尔和合著者的正规潜力。本质谱覆盖由适当的一维比较算子确定的半线;它是后者间隙中的稠密纯点。如果相互作用是径向周期性的，则存在绝对连续的带;与常规情况相反，在高能极限下，p. p.段的测度不为零。
英文摘要：
We consider Schrödinger 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.
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