{"paper":{"title":"Spectral theory of elliptic differential operators with indefinite weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Jussi Behrndt","submitted_at":"2011-12-14T17:34:19Z","abstract_excerpt":"The spectral properties of a class of non-selfadjoint second order elliptic operators with indefinite weight functions on unbounded domains $\\Omega$ are investigated. It is shown that under an abstract regularity assumption the nonreal spectrum of the associated elliptic operator in $L^2(\\Omega)$ is bounded. In the special case that $\\Omega=R^n $decomposes into subdomains $\\Omega_+$ and $\\Omega_-$ with smooth compact boundaries and the weight function is positive on $\\Omega_+$ and negative on $\\Omega_-$, it turns out that the nonreal spectrum consists only of normal eigenvalues which can be ch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3283","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"}