English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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

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