{"paper":{"title":"Bethe-Sommerfeld conjecture in semiclassical settings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Victor Ivrii","submitted_at":"2019-02-01T14:01:59Z","abstract_excerpt":"Under certain assumptions (including $d\\ge 2)$ we prove that the spectrum of a scalar operator in $\\mathscr{L}^2(\\mathbb{R}^d)$ \\begin{equation*} A_\\varepsilon (x,hD)= A^0(hD) + \\varepsilon B(x,hD), \\end{equation*} covers interval $(\\tau-\\epsilon,\\tau+\\epsilon)$, where $A^0$ is an elliptic operator and $B(x,hD)$ is a periodic perturbation, $\\varepsilon=O(h^\\varkappa)$, $\\varkappa>0$.\n  Further, we consider generalizations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00335","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"}