{"paper":{"title":"Spectral asymptotics for the semiclassical Dirichlet to Neumann operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Andrew Hassell, Victor Ivrii","submitted_at":"2015-05-19T07:22:29Z","abstract_excerpt":"Let $M$ be a compact Riemannian manifold with smooth boundary, and let $R(\\lambda)$ be the Dirichlet-to-Neumann operator at frequency $\\lambda$. We obtain a leading asymptotic for the spectral counting function for $\\lambda^{-1}R(\\lambda)$ in an interval $[a_1, a_2)$ as $\\lambda \\to \\infty$, under the assumption that the measure of periodic billiards on $T^*M$ is zero. The asymptotic takes the form \\begin{equation*} N(\\lambda; a_1,a_2) = \\bigl(\\kappa(a_2)-\\kappa(a_1)\\bigr)\\mathsf{vol}'(\\partial M) \\lambda^{d-1}+o(\\lambda^{d-1}), \\end{equation*} where $\\kappa(a)$ is given explicitly by \\begin{e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04894","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"}