{"paper":{"title":"Spectrum of a singularly perturbed periodic thin waveguide","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":"2016-08-01T14:15:31Z","abstract_excerpt":"We consider a family $\\{\\Omega^\\varepsilon\\}_{\\varepsilon>0}$ of periodic domains in $\\mathbb{R}^2$ with waveguide geometry and analyse spectral properties of the Neumann Laplacian $-\\Delta_{\\Omega^\\varepsilon}$ on $\\Omega^\\varepsilon$. The waveguide $\\Omega^\\varepsilon$ is a union of a thin straight strip of the width $\\varepsilon$ and a family of small protuberances with the so-called \"room-and-passage\" geometry. The protuberances are attached periodically, with a period $\\varepsilon$, along the strip upper boundary. For $\\varepsilon\\to 0$ we prove a (kind of) resolvent convergence of $-\\Del"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00440","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"}