{"paper":{"title":"One-dimensional Schr\\\"odinger operators with $\\delta'$-interactions on a set of Lebesgue measure zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"Johannes F. Brasche, Leonid Nizhnik","submitted_at":"2011-12-12T13:39:54Z","abstract_excerpt":"We give an abstract definition of a one-dimensional Schr\\\"odinger\n  operator with $\\delta'$-interaction on an arbitrary set~$\\Gamma$ of\n  Lebesgue measure zero. The number of negative eigenvalues of such an\n  operator is at least as large as the number of those isolated points\n  of the set~$\\Gamma$ that have negative values of the intensity\n  constants of the $\\delta'$-interaction. In the case where the\n  set~$\\Gamma$ is endowed with a Radon measure, we give constructive\n  examples of such operators having an infinite number of negative eigenvalues."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2545","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"}