{"paper":{"title":"Example of periodic Neumann waveguide with gap in spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Andrii Khrabustovskyi, Giuseppe Cardone","submitted_at":"2016-05-25T10:22:31Z","abstract_excerpt":"In this note we investigate spectral properties of a periodic waveguide $\\Omega^\\varepsilon$ ($\\varepsilon$ is a small parameter) obtained from a straight strip by attaching an array of $\\varepsilon$-periodically distributed identical protuberances having \"room-and-passage\" geometry. In the current work we consider the operator $\\mathcal{A}^\\varepsilon=-\\rho^\\varepsilon\\Delta_{\\Omega^\\varepsilon}$, where $\\Delta_{\\Omega^\\varepsilon}$ is the Neumann Laplacian in $\\Omega^\\varepsilon$, the weight $\\rho^\\varepsilon$ is equal to $1$ everywhere except the union of the \"rooms\". We will prove that the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07812","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"}