Geodesic
Absence of Eigenvalues for the Periodic Schr\"odinger Operator with Singular Potential in a Rectangular Cylinder
Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 2, pp. 27-37

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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 $\sigma(x,y)\delta_{\Sigma}(x,y)$, where $\Sigma$ is a periodic system of hypersurfaces. We establish that there are no eigenvalues in the spectrum of this operator, provided that $\Sigma$ is sufficiently smooth and $\sigma\in L_{p,\operatorname{loc}}(\Sigma)$, $p>d-1$.
Keywords: Schrödinger operator, periodic coefficients, absolutely continuous spectrum. 
@article{FAA_2013_47_2_a3,
     author = {I. Kachkovskii},
     title = {Absence of {Eigenvalues} for the {Periodic} {Schr\"odinger} {Operator} with {Singular} {Potential} in a {Rectangular} {Cylinder}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {27--37},
     publisher = {mathdoc},
     volume = {47},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2013_47_2_a3/}
}
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I. Kachkovskii. Absence of Eigenvalues for the Periodic Schr\"odinger Operator with Singular Potential in a Rectangular Cylinder. Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 2, pp. 27-37. http://geodesic.mathdoc.fr/item/FAA_2013_47_2_a3/