Schrödinger Operators with Periodic Singular Potentials

Abstract

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

References in corpus (1)

• Schrödinger operators with singular Gordon potentials

Cited by in corpus (6)

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• Spectra of Schroedinger operators on equilateral quantum graphs
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• Inverse spectral problems for energy-dependent Sturm-Liouville equations
• Schrödinger operators with singular Gordon potentials
• Singularly perturbed periodic and semiperiodic differential operators