{"paper":{"title":"Analysis of the Hodge Laplacian on the Heisenberg group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Detlef M\\\"uller, Fulvio Ricci, Marco M. Peloso","submitted_at":"2012-06-20T15:37:23Z","abstract_excerpt":"We consider the Hodge Laplacian $\\Delta$ on the Heisenberg group $H_n$, endowed with a left-invariant and U(n)-invariant Riemannian metric. For $0\\le k\\le 2n+1$, let $\\Delta_k$ denote the Hodge Laplacian restricted to $k$-forms.\n  Our first main result shows that $L^2\\Lambda^k(H_n)$ decomposes into finitely many mutually orthogonal subspaces $\\V_\\nu$ with the properties: {itemize} $\\dom \\Delta_k$ splits along the $\\V_\\nu$'s as $\\sum_\\nu(\\dom\\Delta_k\\cap \\V_\\nu)$; $\\Delta_k:(\\dom\\Delta_k\\cap \\V_\\nu)\\longrightarrow \\V_\\nu$ for every $\\nu$; for each $\\nu$, there is a Hilbert space $\\cH_\\nu$ of $L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4540","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"}