{"paper":{"title":"Spectral bounds for singular indefinite Sturm-Liouville operators with $L^1$--potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Carsten Trunk, Jussi Behrndt, Philipp Schmitz","submitted_at":"2017-09-14T22:08:14Z","abstract_excerpt":"The spectrum of the singular indefinite Sturm-Liouville operator $$A=\\text{\\rm sgn}(\\cdot)\\bigl(-\\tfrac{d^2}{dx^2}+q\\bigr)$$ with a real potential $q\\in L^1(\\mathbb R)$ covers the whole real line and, in addition, non-real eigenvalues may appear if the potential $q$ assumes negative values. A quantitative analysis of the non-real eigenvalues is a challenging problem, and so far only partial results in this direction were obtained. In this paper the bound $$|\\lambda|\\leq |q|_{L^1}^2$$ on the absolute values of the non-real eigenvalues $\\lambda$ of $A$ is obtained. Furthermore, separate bounds o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04994","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"}