Unique continuation and lifting of spectral band edges of Schr\"odinger operators on unbounded domains (With an Appendix by Albrecht Seelmann)

Ivica Nakić; Matthias Täufer; Martin Tautenhahn; Ivan Veselic; Albrecht Seelmann

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arXiv · 1804.07816

Unique continuation and lifting of spectral band edges of Schr\"odinger operators on unbounded domains (With an Appendix by Albrecht Seelmann)

Ivica Nakić·Matthias Täufer·Martin Tautenhahn·Ivan Veselic·Albrecht Seelmann

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Abstract

We prove and apply two theorems: First, a quantitative, scale-free unique continuation estimate for functions in a spectral subspace of a Schr\"odinger operator on a bounded or unbounded domain, second, a perturbation and lifting estimate for edges of the essential spectrum of a self-adjoint operator under a semi-definite perturbation. These two results are combined to obtain lower and upper Lipschitz bounds on the function parametrizing locally a chosen edge of the essential spectrum of a Schr\"odinger operator in dependence of a coupling constant. Analogous estimates for eigenvalues, possibly in gaps of the essential spectrum, are exhibited as well.

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BibTeX RIS

Ivica Nakić, Matthias Täufer, Martin Tautenhahn, Ivan Veselic, Albrecht Seelmann. 2018-04-20. Unique continuation and lifting of spectral band edges of Schr\"odinger operators on unbounded domains (With an Appendix by Albrecht Seelmann). https://arxiv.org/abs/1804.07816

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