{"paper":{"title":"$J$-class weighted translations on locally compact groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"A. R. Imanzadeh Fard, I. Akbarbaglu, M. R. Azimi","submitted_at":"2025-06-05T08:04:53Z","abstract_excerpt":"A bounded linear operator $T$ on a Banach space $X$ (not necessarily separable) is said to be $J$-class operator whenever the extended limit set, say $J_T(x)$ equals $X$ for some vector $x\\in X$. Practically, the extended limit sets localize the dynamical behavior of operators. In this paper, using the extended limit sets we will examine the necessary and sufficient conditions for the weighted translation $T_{a,\\omega}$ to be $J$-class on a locally compact group $G$, within the setting of $ L^p$-spaces for $ 1 \\leq p < \\infty $. Precisely, we delineate the boundary between $J$-class and hyperc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04730","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/2506.04730/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"}