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

Autori
Nakić, Ivica ; Täufer, Matthias ; Tautenhahn, Martin ; Veselić, Ivan

Izvornik
Journal of Spectral Theory (1664-039X) 10 (2020), 3; 843-885

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Schrödinger operators ; unique continuation

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA