Schrödinger Operators with Periodic Singular Potentials

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We show that formal Schrödinger operators with singular potentials from the space W^{-1}_{2,unif}(R) can be naturally defined to give selfadjoint and bounded below operators, which depend continuously in the uniform resolvent sense on the potential in the W^{-1}_{2,unif}(R)-norm. In the case of periodic singular potentials we also establish pure absolute continuity and a band and gap structure of the spectrum thus generalising some classical results for singular potentials of one-dimensional quasicrystal theory.
12 pages, Amslatex, To appear in Meth. Funct. Anal. Topol

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Spectral Theory, Mathematical Physics, 34L05 (Primary) 34L40, 47A10, 47B25 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/62224

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0109129
 http://arxiv.org/abs/math/0109129

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arXiv