{"paper":{"title":"Spectral asymptotics for Dirichlet to Neumann operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Victor Ivrii","submitted_at":"2018-02-21T11:38:07Z","abstract_excerpt":"We consider eigenvalues of the Dirichlet-to-Neumann operator for Laplacian in the domain (or manifold) with edges and establish the asymptotics of the eigenvalue counting function \\begin{equation*} \\mathsf{N}(\\lambda)= \\kappa_0\\lambda^d +O(\\lambda^{d-1})\\qquad \\text{as}\\ \\ \\lambda\\to+\\infty, \\end{equation*} where $d$ is dimension of the boundary. Further, in certain cases we establish two-term asymptotics \\begin{equation*} \\mathsf{N}(\\lambda)= \\kappa_0\\lambda^d+\\kappa_1\\lambda^{d-1}+o(\\lambda^{d-1})\\qquad \\text{as}\\ \\ \\lambda\\to+\\infty. \\end{equation*} We also establish improved asymptotics fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07524","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"}