{"paper":{"title":"Heisenberg-Modulation Spaces at the Crossroads of Coorbit Theory and Decomposition Space Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"David Rottensteiner, Michael Ruzhansky, V\\'eronique Fischer","submitted_at":"2018-12-19T11:01:29Z","abstract_excerpt":"We show that generalised time-frequency shifts on the Heisenberg group $\\mathbf{H}_n \\cong \\mathbb{R}^{2n+1}$, realised as a unitary irreducible representation of a nilpotent Lie group acting on $L^{2}(\\mathbf{H}_n)$, give rise to a novel type of function spaces on $\\mathbb{R}^{2n+1}$. The representation we employ is the generic unitary irreducible representation of the $3$-step nilpotent Dynin-Folland group.\n  In doing so, we answer the question whether representations of nilpotent Lie groups ever yield coorbit spaces distinct from the classical modulation spaces $M^{\\mathbf{p}, \\mathbf{q}}_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07876","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"}