Absence of eigenvalues for the periodic Schrödinger operator with singular potential in a rectangular cylinder
Absence of eigenvalues for the periodic Schrödinger operator with singular potential in a rectangular cylinder
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矩形圆柱体中具有奇异势的周期性薛定谔算子不存在特征值
DOI：
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发表时间：
2013
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影响因子：
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通讯作者：
I. Kachkovskiy
中科院分区：
文献类型：
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作者：
I. Kachkovskiy
考虑具有矩形截面的d维圆柱体上的周期Schrödinger算子。电势可以包含形式为σ(x, y)δΣ（x,y）的奇异分量，其中Σ是超曲面的周期系统。在Σ足够光滑且Σ∈Lp，loc（Σ）， p > d−1的条件下，证明了该算子的谱中不存在特征值。
We consider the periodic Schrödinger operator on a d-dimensional cylinder with rectangular section. The electric potential may contain a singular component of the form σ(x, y)δΣ(x,y), where Σ is a periodic system of hypersurfaces. We establish that there are no eigenvalues in the spectrum of this operator, provided that Σ is sufficiently smooth and σ ∈ Lp,loc(Σ), p > d − 1.