{"paper":{"title":"On operator error estimates for homogenization of hyperbolic systems with periodic coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yulia Meshkova","submitted_at":"2017-05-06T21:58:33Z","abstract_excerpt":"In $L_2(\\mathbb{R}^d;\\mathbb{C}^n)$, we consider a selfadjoint matrix strongly elliptic second order differential operator $\\mathcal{A}_\\varepsilon$, $\\varepsilon >0$. The coefficients of the operator $\\mathcal{A}_\\varepsilon$ are periodic and depend on $\\mathbf{x}/\\varepsilon$. We study the behavior of the operator $\\mathcal{A}_\\varepsilon ^{-1/2}\\sin (\\tau \\mathcal{A}_\\varepsilon ^{1/2})$, $\\tau\\in\\mathbb{R}$, in the small period limit. The principal term of approximation in the $(H^1\\rightarrow L_2)$-norm for this operator is found. Approximation in the $(H^2\\rightarrow H^1)$-operator norm "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02531","kind":"arxiv","version":4},"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"}