Unique continuation and lifting of spectral band edges of Schrödinger operators on unbounded domains

  • Ivica Nakić

    University of Zagreb, Croatia
  • Matthias Täufer

    Queen Mary University of London, UK
  • Martin Tautenhahn

    Technische Universität Chemnitz, Germany
  • Ivan Veselić

    Technische Universität Dortmund, Germany
Unique continuation and lifting of spectral band edges of Schrödinger operators on unbounded domains cover
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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 Schrödinger 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 Schrödinger operator in dependence of a coupling constant. Analogous estimates for eigenvalues, possibly in gaps of the essential spectrum, are exhibited as well.

Cite this article

Ivica Nakić, Matthias Täufer, Martin Tautenhahn, Ivan Veselić, Unique continuation and lifting of spectral band edges of Schrödinger operators on unbounded domains. J. Spectr. Theory 10 (2020), no. 3, pp. 843–885

DOI 10.4171/JST/314