{"paper":{"title":"Complete Semiclassical Spectral Asymptotics for Periodic and Almost Periodic Perturbations of Constant Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Victor Ivrii","submitted_at":"2018-08-05T14:09:05Z","abstract_excerpt":"Under certain assumptions we derive a complete semiclassical asymptotics of the spectral function $e_{h,\\varepsilon}(x,x,\\lambda)$ for a scalar operator\n  \\begin{equation*} A_\\varepsilon (x,hD)= A^0(hD) + \\varepsilon B(x,hD), \\end{equation*} where $A^0$ is an elliptic operator and $B(x,hD)$ is a periodic or almost periodic perturbation.\n  In particular, a complete semiclassical asymptotics of the integrated density of states also holds. Further, we consider generalizations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01619","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"}