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It is assumed that the function $\\mu(\\x,\\y)$ is $\\Z^d$-periodic in each variable, $\\mu(\\x,\\y)=\\mu(\\y,\\x)$ for all $\\x$ and $\\y$, and $0< \\mu_- \\leqslant \\mu(\\x,\\y) \\leqslant \\mu_+< \\infty$. Under these assumptions we show that the resolvent $({\\mathbb A}_\\eps + I)^{-1}$ converges, as $\\eps\\to0$, in the operator n"},"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":"2412.20408","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-12-29T09:16:58Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"9b541ddb76bd29c8b7491028275195afd88d90378afa19e2d2e6ca09a9620e50","abstract_canon_sha256":"775e604c6836c66c98fd5bd80ffb33e4b23d293dad4895f3190bd3f51c74db60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:54:58.850299Z","signature_b64":"fWJn8oAmEPyGj0m40ay5yiPU9jL49Dhef0Bxby0jS44er+dZ+sgljh7FbWAYP2q2zbbGrmxcvTFtoRpPTexKDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fec23f12274162d4e9257e5c843cd7abd72c3993fa82705bfe74d513d62204b4","last_reissued_at":"2026-07-05T09:54:58.849834Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:54:58.849834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Operator estimates in homogenization of L\\'evy-type operators with periodic coefficients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Andrey Piatnitski, Elena Zhizhina, Tatiana Suslina, Vladimir Sloushch","submitted_at":"2024-12-29T09:16:58Z","abstract_excerpt":"The paper deals with homogenization of self-adjoint operators in $L_2(\\mathbb R^d)$ of the form $$ ({\\mathbb A}_\\eps u) (\\x) = \\int_{\\R^d} \\mu(\\x/\\eps, \\y/\\eps) \\frac{\\left( u(\\x) - u(\\y) \\right)}{|\\x - \\y|^{d+\\alpha}}\\,d\\y, $$ where $0< \\alpha < 2$, and $\\eps>0$ is a small parameter. It is assumed that the function $\\mu(\\x,\\y)$ is $\\Z^d$-periodic in each variable, $\\mu(\\x,\\y)=\\mu(\\y,\\x)$ for all $\\x$ and $\\y$, and $0< \\mu_- \\leqslant \\mu(\\x,\\y) \\leqslant \\mu_+< \\infty$. Under these assumptions we show that the resolvent $({\\mathbb A}_\\eps + I)^{-1}$ converges, as $\\eps\\to0$, in the operator n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.20408","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.20408/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2412.20408","created_at":"2026-07-05T09:54:58.849890+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.20408v1","created_at":"2026-07-05T09:54:58.849890+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.20408","created_at":"2026-07-05T09:54:58.849890+00:00"},{"alias_kind":"pith_short_12","alias_value":"73BD6ERHIFRN","created_at":"2026-07-05T09:54:58.849890+00:00"},{"alias_kind":"pith_short_16","alias_value":"73BD6ERHIFRNJ2JF","created_at":"2026-07-05T09:54:58.849890+00:00"},{"alias_kind":"pith_short_8","alias_value":"73BD6ERH","created_at":"2026-07-05T09:54:58.849890+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.29131","citing_title":"High-order convergence rates of periodic homogenization for symmetric L\\'evy type operators","ref_index":42,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/73BD6ERHIFRNJ2JFPZOIIPGXVP","json":"https://pith.science/pith/73BD6ERHIFRNJ2JFPZOIIPGXVP.json","graph_json":"https://pith.science/api/pith-number/73BD6ERHIFRNJ2JFPZOIIPGXVP/graph.json","events_json":"https://pith.science/api/pith-number/73BD6ERHIFRNJ2JFPZOIIPGXVP/events.json","paper":"https://pith.science/paper/73BD6ERH"},"agent_actions":{"view_html":"https://pith.science/pith/73BD6ERHIFRNJ2JFPZOIIPGXVP","download_json":"https://pith.science/pith/73BD6ERHIFRNJ2JFPZOIIPGXVP.json","view_paper":"https://pith.science/paper/73BD6ERH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.20408&json=true","fetch_graph":"https://pith.science/api/pith-number/73BD6ERHIFRNJ2JFPZOIIPGXVP/graph.json","fetch_events":"https://pith.science/api/pith-number/73BD6ERHIFRNJ2JFPZOIIPGXVP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/73BD6ERHIFRNJ2JFPZOIIPGXVP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/73BD6ERHIFRNJ2JFPZOIIPGXVP/action/storage_attestation","attest_author":"https://pith.science/pith/73BD6ERHIFRNJ2JFPZOIIPGXVP/action/author_attestation","sign_citation":"https://pith.science/pith/73BD6ERHIFRNJ2JFPZOIIPGXVP/action/citation_signature","submit_replication":"https://pith.science/pith/73BD6ERHIFRNJ2JFPZOIIPGXVP/action/replication_record"}},"created_at":"2026-07-05T09:54:58.849890+00:00","updated_at":"2026-07-05T09:54:58.849890+00:00"}