{"paper":{"title":"Some spectral properties of Rooms and Passages domains and their skeletons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"B.M. Brown, I.G. Wood, W.D. Evans","submitted_at":"2013-01-18T14:59:29Z","abstract_excerpt":"In this paper we investigate spectral properties of Lapla- cians on Rooms and Passages domains. In the first part, we use Dirichlet- Neumann bracketing techniques to show that for the Neumann Lapla- cian in certain Rooms and Passages domains the second term of the asymptotic expansion of the counting function is of order $\\sqrt{\\lambda}$. For the Dirichlet Laplacian our methods only give an upper estimate of the form $\\sqrt{\\lambda}$. In the second part of the paper, we consider the relation- ship between Neumann Laplacians on Rooms and Passages domains and Sturm-Liouville operators on the ske"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4396","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"}