{"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"}