{"paper":{"title":"An eigenvalue inequality for Schr\\\"odinger operators with $\\delta$ and $\\delta'$-interactions supported on hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Jonathan Rohleder, Vladimir Lotoreichik","submitted_at":"2014-07-21T15:48:35Z","abstract_excerpt":"We consider self-adjoint Schr\\\"odinger operators in $L^2 (\\mathbb{R}^d)$ with a $\\delta$-interaction of strength $\\alpha$ and a $\\delta'$-interaction of strength $\\beta$, respectively, supported on a hypersurface, where $\\alpha$ and $\\beta^{-1}$ are bounded, real-valued functions. It is known that the inequality $0 < \\beta \\leq 4/\\alpha$ implies inequality of the eigenvalues of these two operators below the bottoms of the essential spectra. We show that this eigenvalue inequality is strict whenever $\\beta < 4 / \\alpha$ on a nonempty, open subset of the hypersurface. Moreover, we point out spec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5539","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"}