{"paper":{"title":"Approximations of spectra of Schr\\\"odinger operators with complex potentials on $\\mathbb{R}^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"Christiane Tretter, Petr Siegl, Sabine B\\\"ogli","submitted_at":"2015-12-06T20:00:45Z","abstract_excerpt":"We study spectral approximations of Schr\\\"odinger operators $T=-\\Delta+Q$ with complex potentials on $\\Omega=\\mathbb{R}^d$, or exterior domains $\\Omega\\subset \\mathbb{R}^d$, by domain truncation. Our weak assumptions cover wide classes of potentials $Q$ for which $T$ has discrete spectrum, of approximating domains $\\Omega_n$, and of boundary conditions on $\\partial \\Omega_n$ such as mixed Dirichlet/Robin type. In particular, ${\\rm Re} \\, Q$ need not be bounded from below and $Q$ may be singular. We prove generalized norm resolvent convergence and spectral exactness, i.e. approximation of all e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01826","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"}