{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:4EPNPXQBNDOGNUHUEWOQIUCOHE","short_pith_number":"pith:4EPNPXQB","schema_version":"1.0","canonical_sha256":"e11ed7de0168dc66d0f4259d04504e3909afa91e078299d4bb86e4371eb2c117","source":{"kind":"arxiv","id":"1705.02531","version":4},"attestation_state":"computed","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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1705.02531","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-06T21:58:33Z","cross_cats_sorted":[],"title_canon_sha256":"4417c140b3de195d16279e9e8356e22a110078bfcdc7feeb468d43cf34f7b9ce","abstract_canon_sha256":"67de5e99566b3e61f1bc072f4e4b90785fb08babdab4e52970913601f94cd1d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:04.103435Z","signature_b64":"dEwiAleFNxRbsKVQLFBrHOI/8AyajHIP45yo61t4VZhQtjeTxD0a1KL/8uyYXkOqO0wdYoi5Tnop+WZcxqb8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e11ed7de0168dc66d0f4259d04504e3909afa91e078299d4bb86e4371eb2c117","last_reissued_at":"2026-05-18T00:19:04.102893Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:04.102893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1705.02531","created_at":"2026-05-18T00:19:04.102974+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.02531v4","created_at":"2026-05-18T00:19:04.102974+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02531","created_at":"2026-05-18T00:19:04.102974+00:00"},{"alias_kind":"pith_short_12","alias_value":"4EPNPXQBNDOG","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_16","alias_value":"4EPNPXQBNDOGNUHU","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_8","alias_value":"4EPNPXQB","created_at":"2026-05-18T12:30:58.224056+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4EPNPXQBNDOGNUHUEWOQIUCOHE","json":"https://pith.science/pith/4EPNPXQBNDOGNUHUEWOQIUCOHE.json","graph_json":"https://pith.science/api/pith-number/4EPNPXQBNDOGNUHUEWOQIUCOHE/graph.json","events_json":"https://pith.science/api/pith-number/4EPNPXQBNDOGNUHUEWOQIUCOHE/events.json","paper":"https://pith.science/paper/4EPNPXQB"},"agent_actions":{"view_html":"https://pith.science/pith/4EPNPXQBNDOGNUHUEWOQIUCOHE","download_json":"https://pith.science/pith/4EPNPXQBNDOGNUHUEWOQIUCOHE.json","view_paper":"https://pith.science/paper/4EPNPXQB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.02531&json=true","fetch_graph":"https://pith.science/api/pith-number/4EPNPXQBNDOGNUHUEWOQIUCOHE/graph.json","fetch_events":"https://pith.science/api/pith-number/4EPNPXQBNDOGNUHUEWOQIUCOHE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4EPNPXQBNDOGNUHUEWOQIUCOHE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4EPNPXQBNDOGNUHUEWOQIUCOHE/action/storage_attestation","attest_author":"https://pith.science/pith/4EPNPXQBNDOGNUHUEWOQIUCOHE/action/author_attestation","sign_citation":"https://pith.science/pith/4EPNPXQBNDOGNUHUEWOQIUCOHE/action/citation_signature","submit_replication":"https://pith.science/pith/4EPNPXQBNDOGNUHUEWOQIUCOHE/action/replication_record"}},"created_at":"2026-05-18T00:19:04.102974+00:00","updated_at":"2026-05-18T00:19:04.102974+00:00"}