Unique continuation and lifting of spectral band edges of Schrödinger operators on unbounded domains (CROSBI ID 261187)
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Nakić, Ivica ; Täufer, Matthias ; Tautenhahn, Martin ; Veselić, Ivan
engleski
Unique continuation and lifting of spectral band edges of Schrödinger operators on unbounded domains
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.
Schrödinger operators ; unique continuation
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