{"paper":{"title":"On large potential perturbations of the Schr\\\"odinger, wave and Klein--Gordon equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Piero D'Ancona","submitted_at":"2017-06-15T12:24:47Z","abstract_excerpt":"We prove a sharp resolvent estimate in scale invariant norms of Amgon--H\\\"{o}rmander type for a magnetic Schr\\\"{o}dinger operator on $\\mathbb{R}^{n}$, $n\\ge3$\\begin{equation*} L=-(\\partial+iA)^{2}+V \\end{equation*}with large potentials $A,V$ of almost critical decay and regularity.\n  The estimate is applied to prove sharp smoothing and Strichartz estimates for the Schr\\\"{o}dinger, wave and Klein--Gordon flows associated to $L$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04840","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"}