{"paper":{"title":"Application of signal analysis to the embedding problem of $\\mathbb{Z}^k$-actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.CV","math.IT"],"primary_cat":"math.DS","authors_text":"Masaki Tsukamoto, Yixiao Qiao, Yonatan Gutman","submitted_at":"2017-09-01T01:15:31Z","abstract_excerpt":"We study the problem of embedding arbitrary $\\mathbb{Z}^k$-actions into the shift action on the infinite dimensional cube $\\left([0,1]^D\\right)^{\\mathbb{Z}^k}$. We prove that if a $\\mathbb{Z}^k$-action satisfies the marker property (in particular if it is a minimal system without periodic points) and if its mean dimension is smaller than $D/2$ then we can embed it in the shift on $\\left([0,1]^D\\right)^{\\mathbb{Z}^k}$. The value $D/2$ here is optimal. The proof goes through signal analysis. We develop the theory of encoding $\\mathbb{Z}^k$-actions into band-limited signals and apply it to provin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00125","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":""},"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"}