{"paper":{"title":"Homogenization of non-symmetric convolution type operators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Andrey Piatnitski, Elena Zhizhina, Tatiana Suslina, Vladimir Sloushch","submitted_at":"2025-06-08T14:50:52Z","abstract_excerpt":"The paper studies homogenization problem for a bounded in $L_2(\\mathbb R^d)$ convolution type operator ${\\mathbb A}_\\eps$, $\\eps >0$, of the form $$ ({\\mathbb A}_\\eps u) (\\x) = \\eps^{-d-2} \\int_{\\R^d} a((\\x-\\y)/\\eps) \\mu(\\x/\\eps, \\y/\\eps) \\left( u(\\x) - u(\\y) \\right)\\,d\\y. $$ It is assumed that $a(\\x)$ is a non-negative function from $L_1(\\R^d)$, and $\\mu(\\x,\\y)$ is a periodic in $\\x$ and $\\y$ function such that $0< \\mu_- \\leqslant \\mu(\\x,\\y) \\leqslant \\mu_+< \\infty$. No symmetry assumption on $a(\\cdot)$ and $\\mu(\\cdot)$ is imposed, so the operator ${\\mathbb A}_\\eps$ need not be self-adjoint. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07176","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/2506.07176/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"}