{"paper":{"title":"Bethe-Sommerfeld conjecture for periodic operators with strong perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"A.V. Sobolev, L. Parnovski","submitted_at":"2009-07-05T20:27:09Z","abstract_excerpt":"We consider a periodic self-adjoint pseudo-differential operator $H=(-\\Delta)^m+B$, $m>0$, in $\\R^d$ which satisfies the following conditions: (i) the symbol of $B$ is smooth in $\\bx$, and (ii) the perturbation $B$ has order less than $2m$. Under these assumptions, we prove that the spectrum of $H$ contains a half-line. This, in particular implies the Bethe-Sommerfeld Conjecture for the Schr\\\"odinger operator with a periodic magnetic potential in all dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0887","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"}