{"paper":{"title":"Homogenization of nonlocal convolution type operators: Approximation for the resolvent with corrector","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.AP","authors_text":"Andrei Piatnitski, Elena Zhizhina, Tatiana Suslina, Vladimir Sloushch","submitted_at":"2023-11-28T07:32:02Z","abstract_excerpt":"In $L_2(\\mathbb{R}^d)$, we consider a selfadjoint bounded operator ${\\mathbb A}_\\varepsilon$, $\\varepsilon >0$, of the form $$ ({\\mathbb A}_\\varepsilon u) (\\mathbf{x}) = \\varepsilon^{-d-2} \\int_{\\mathbb{R}^d} a((\\mathbf{x} - \\mathbf{y} )/ \\varepsilon ) \\mu(\\mathbf{x} /\\varepsilon, \\mathbf{y} /\\varepsilon) \\left( u(\\mathbf{x}) - u(\\mathbf{y}) \\right)\\, d\\mathbf{y}. $$ It is assumed that $a(\\mathbf{x})$ is a nonnegative function of class $L_1(\\mathbb{R}^d)$ such that \\hbox{$a(-\\mathbf{x}) = a(\\mathbf{x})$} and $\\mu(\\mathbf{x},\\mathbf{y})$ is $\\mathbb{Z}^d$-periodic in each variable and such that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.16574","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/2311.16574/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"}