{"paper":{"title":"On the domain of a magnetic Schr\\\"odinger operator with complex electric potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"B Helffer (LMJL, Jean Nourrigat (LMR), LMO)","submitted_at":"2017-09-25T15:15:40Z","abstract_excerpt":"The aim of this paper is to review and compare the spectral properties of (the closed extension of) --$\\Delta$ + U (V $\\ge$ 0) and --$\\Delta$ + iV in L 2 (R^d) for C $\\infty$ real potentials U or V with polynomial behavior. The case with magnetic field will be also considered. More precisely, we would like to present the existing criteria for: $\\bullet$ essential selfadjointness or maximal accretivity $\\bullet$ Compactness of the resolvent. $\\bullet$ Maximal inequalities, i.e. the existence of C > 0 such that, $\\forall$u $\\in$ C^$\\infty$\\_0 (R ^d), ||u||^2 \\_{H^2 (R^d)} + ||U u||^2 \\_{L^2 (R^d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08542","kind":"arxiv","version":1},"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"}