{"paper":{"title":"Resolvent estimates for one-dimensional Schr\\\"odinger operators with complex potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"Antonio Arnal, Petr Siegl","submitted_at":"2022-03-29T22:40:40Z","abstract_excerpt":"We study one-dimensional Schr\\\"odinger operators $\\operatorname{H} = -\\partial_x^2 + V$ with unbounded complex potentials $V$ and derive asymptotic estimates for the norm of the resolvent, $\\Psi(\\lambda) := \\| (\\operatorname{H} - \\lambda)^{-1} \\|$, as $|\\lambda| \\to +\\infty$, separately considering $\\lambda \\in \\operatorname{Ran} V$ and $\\lambda \\in \\mathbb{R}_+$. In each case, our analysis yields an exact leading order term and an explicit remainder for $\\Psi(\\lambda)$ and we show these estimates to be optimal. We also discuss several extensions of the main results, their interrelation with s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.15938","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.15938/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}