Schrödinger Operators with Periodic Singular Potentials

Rostyslav O. Hryniv; Yaroslav V. Mykytyuk

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Schrödinger Operators with Periodic Singular Potentials

Rostyslav O. Hryniv·Yaroslav V. Mykytyuk

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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.

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BibTeX RIS

Rostyslav O. Hryniv, Yaroslav V. Mykytyuk. 2001-09-19. Schrödinger Operators with Periodic Singular Potentials. https://arxiv.org/abs/math/0109129

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