{"paper":{"title":"Eigenvalues of Robin Laplacians in infinite sectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Konstantin Pankrashkin, Magda Khalile","submitted_at":"2016-07-22T21:35:01Z","abstract_excerpt":"For $\\alpha\\in(0,\\pi)$, let $U_\\alpha$ denote the infinite planar sector of opening $2\\alpha$, \\[ U_\\alpha=\\big\\{ (x_1,x_2)\\in\\mathbb R^2: \\big|\\arg(x_1+ix_2) \\big|<\\alpha \\big\\}, \\] and $T^\\gamma_\\alpha$ be the Laplacian in $L^2(U_\\alpha)$, $T^\\gamma_\\alpha u= -\\Delta u$, with the Robin boundary condition $\\partial_\\nu u=\\gamma u$, where $\\partial_\\nu$ stands for the outer normal derivative and $\\gamma>0$. The essential spectrum of $T^\\gamma_\\alpha$ does not depend on the angle $\\alpha$ and equals $[-\\gamma^2,+\\infty)$, and the discrete spectrum is non-empty iff $\\alpha<\\frac\\pi 2$. In this c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06848","kind":"arxiv","version":2},"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"}