{"paper":{"title":"Semiclassical resolvent estimates for bounded potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.AP","authors_text":"Fr\\'ed\\'eric Klopp, Martin Vogel","submitted_at":"2018-03-06T22:32:25Z","abstract_excerpt":"We study the cut-off resolvent of semiclassical Schr{\\\"o}dinger operators on $\\mathbb{R}^d$ with bounded compactly supported potentials $V$. We prove that for real energies $\\lambda^2$ in a compact interval in $\\mathbb{R}_+$ and for any smooth cut-off function $\\chi$ supported in a ball near the support of the potential $V$, for some constant $C>0$, one has\n  \\begin{equation*}\n  \\| \\chi (-h^2\\Delta + V-\\lambda^2)^{-1} \\chi \\|_{L^2\\to H^1} \\leq C\n  \\,\\mathrm{e}^{Ch^{-4/3}\\log \\frac{1}{h} }.\n  \\end{equation*} This bound shows in particular an upper bound on the imaginary parts of the resonances "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02450","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"}