{"paper":{"title":"Unique continuation principle for spectral projections of Schr\\\" odinger operators and optimal Wegner estimates for non-ergodic random Schr\\\" odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Abel Klein","submitted_at":"2012-09-21T17:12:30Z","abstract_excerpt":"We prove a unique continuation principle for spectral projections of Schr\\\" odinger operators. We consider a Schr\\\" odinger operator $H= -\\Delta + V$ on $\\mathrm{L}^2(\\mathbb{R}^d)$, and let $H_{\\Lambda}$ denote its restriction to a finite box $\\Lambda$ with either Dirichlet or periodic boundary condition. We prove unique continuation estimates of the type $\\chi_I (H_\\Lambda) W \\chi_I (H_\\Lambda) \\ge \\kappa\\, \\chi_I (H_\\Lambda) $ with $\\kappa >0$ for appropriate potentials $W\\ge 0$ and intervals $I$. As an application, we obtain optimal Wegner estimates at all energies for a class of non-ergod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4863","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}