{"paper":{"title":"Scale-free and quantitative unique continuation for infinite dimensional spectral subspaces of Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Martin Tautenhahn, Matthias T\\\"aufer","submitted_at":"2016-09-23T15:50:58Z","abstract_excerpt":"We prove a quantitative unique continuation principle for infinite dimensional spectral subspaces of Schr\\\"odinger operators. Let $\\Lambda_L = (-L/2,L/2)^d$ and $H_L = -\\Delta_L + V_L$ be a Schr\\\"odinger operator on $L^2 (\\Lambda_L)$ with a bounded potential $V_L : \\Lambda_L \\to \\mathbb{R}^d$ and Dirichlet, Neumann, or periodic boundary conditions. Our main result is of the type\n  \\[\n  \\int_{\\Lambda_L} \\lvert \\phi \\rvert^2 \\leq C_{\\mathrm{sfuc}} \\int_{W_\\delta (L)} \\lvert \\phi \\rvert^2,\n  \\] where $\\phi$ is an infinite complex linear combination of eigenfunctions of $H_L$ with exponentially de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07408","kind":"arxiv","version":2},"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"}