{"paper":{"title":"Spectral theory of semibounded Schr\\\"odinger operators with $\\delta'$-interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Aleksey Kostenko, Mark Malamud","submitted_at":"2012-12-07T19:45:40Z","abstract_excerpt":"We study spectral properties of Hamiltonians $\\rH_{X,\\gB,q}$ with $\\delta'$-point interactions on a discrete set $X={x_k}_{k=1}^\\infty\\subset\\R_+$. %at the centers $x_n$ on the positive half line in terms of energy forms. Using the form approach, we establish analogs of some classical results on operators $\\rH_q=-d^2/dx^2+q$ with locally integrable potentials $q\\in L^1_{\\loc}(\\R_+)$. In particular, we establish analogues of the Glazman-Povzner-Wienholtz theorem, the Molchanov discreteness criterion, and the Birman theorem on stability of an essential spectrum. It turns out that in contrast to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1691","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"}