{"paper":{"title":"The $m$th order Orlicz projection bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Deping Ye, Xia Zhou, Zengle Zhang","submitted_at":"2025-01-13T18:53:56Z","abstract_excerpt":"Let $M_{n, m}(\\mathbb{R})$ be the space of $n\\times m$ real matrices. Define $\\mathcal{K}_o^{n,m}$ as the set of convex compact subsets in $M_{n,m}(\\mathbb{R})$ with nonempty interior containing the origin $o\\in M_{n, m}(\\mathbb{R})$, and $\\mathcal{K}_{(o)}^{n,m}$ as the members of $\\mathcal{K}_o^{n,m}$ containing $o$ in their interiors. Let $\\Phi: M_{1, m}(\\mathbb{R}) \\rightarrow [0, \\infty)$ be a convex function such that $\\Phi(o)=0$ and $\\Phi(z)+\\Phi(-z)>0$ for $z\\neq o.$ In this paper, we propose the $m$th order Orlicz projection operator $\\Pi_{\\Phi}^m: \\mathcal{K}_{(o)}^{n,1}\\rightarrow \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.07565","kind":"arxiv","version":2},"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/2501.07565/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"}