{"paper":{"title":"Periodic elliptic operators with asymptotically preassigned spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Andrii Khrabustovskyi","submitted_at":"2012-01-18T09:24:49Z","abstract_excerpt":"We deal with operators in $\\mathbb{R}^n$ of the form $$\\mathbf{A}=-{1\\over \\mathbf{b}(x)}\\sum\\limits_{k=1}^n\\ds{\\partial\\over\\partial x_k}(\\mathbf{a}(x){\\partial \\over\\partial x_k})$$ where $\\mathbf{a}(x),\\mathbf{b}(x)$ are positive, bounded and periodic functions. We denote by $\\mathbf{L}_{\\mathrm{per}}$ the set of such operators. The main result of this work is as follows: for an arbitrary $L>0$ and for arbitrary pairwise disjoint intervals $(\\alpha_j,\\beta_j)\\subset[0,L]$, $j=1,...,m$ ($m\\in\\mathbb{N}$) we construct the family of operators $\\{\\mathbf{A}^\\varepsilon\\in \\mathbf{L}_{\\mathrm{pe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3729","kind":"arxiv","version":2},"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"}