Schrödinger Operators with Periodic Singular Potentials

Details Schrödinger Operators with Periodic Singular Potentials Schrödinger Operators with Periodic Singular Potentials

2001-09-19

arxiv.org/abs/math/0109129v1

Mathematics

Spectral Theory

12 pages, Amslatex, To appear in Meth. Funct. Anal. Topol

Scientific paper

We show that formal Schr\"odinger 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.

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