{"paper":{"title":"Exhaustive families of representations of $C^*$-algebras associated to $N$-body Hamiltonians with asymptotically homogeneous interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jeremy Mougel, Nicolas Prudhon","submitted_at":"2018-12-17T11:24:43Z","abstract_excerpt":"We continue the analysis of algebras introduced by Georgescu, Nistor and their coauthors, in order to study $N$-body type Hamiltonians with interactions. More precisely, let $Y$ be a linear subspace of a finite dimensional Euclidean space $X$, and $v_Y$ be a continuous function on $X/Y$ that has uniform homogeneous radial limits at infinity. We consider, in this paper, Hamiltonians of the form $H = - \\Delta + \\sum_{Y \\in S} v_Y$, where the subspaces $Y$ belong to some given family S of subspaces. We prove results on the spectral theory of the Hamiltonian when $S$ is any family of subspaces and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.06704","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"}