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Spectral properties of Schrdinger operators with a strongly attractive delta interaction supported by a surface

Pavel Exner

TBD mathscidoc:1910.43079

arXiv preprint math-ph/0301021, 2003.1
We investigate the operator -\Delta-lpha\delta (x-\Gamma) in -\Delta-lpha\delta (x-\Gamma) , where -\Delta-lpha\delta (x-\Gamma) is a smooth surface which is either compact or periodic and satisfies suitable regularity requirements. We find an asymptotic expansion for the lower part of the spectrum as -\Delta-lpha\delta (x-\Gamma) which involves a``two-dimensional''comparison operator determined by the geometry of the surface -\Delta-lpha\delta (x-\Gamma) . In the compact case the asymptotics concerns negative eigenvalues, in the periodic case Floquet eigenvalues. We also give a bandwidth estimate in the case when a periodic -\Delta-lpha\delta (x-\Gamma) decomposes into compact connected components. Finally, we comment on analogous systems of lower dimension and other aspects of the problem.
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@inproceedings{pavel2003spectral,
  title={Spectral properties of Schrdinger operators with a strongly attractive delta interaction supported by a surface},
  author={Pavel Exner},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020125201848054608},
  booktitle={arXiv preprint math-ph/0301021},
  year={2003},
}
Pavel Exner. Spectral properties of Schrdinger operators with a strongly attractive delta interaction supported by a surface. 2003. In arXiv preprint math-ph/0301021. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020125201848054608.
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