arXiv math/01091292001-09-19math.SPmath-phmath.MP

Schrödinger Operators with Periodic Singular Potentials

Rostyslav O. Hryniv, Yaroslav V. Mykytyuk

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

英文摘要：

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.

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