{"paper":{"title":"A Bound for the Eigenvalue Counting Function for Higher-Order Krein Laplacians on Open Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Ari Laptev, Fritz Gesztesy, Marius Mitrea, Selim Sukhtaiev","submitted_at":"2014-03-15T00:35:17Z","abstract_excerpt":"For an arbitrary nonempty, open set $\\Omega \\subset \\mathbb{R}^n$, $n \\in \\mathbb{N}$, of finite (Euclidean) volume, we consider the minimally defined higher-order Laplacian $(- \\Delta)^m\\big|_{C_0^{\\infty}(\\Omega)}$, $m \\in \\mathbb{N}$, and its Krein--von Neumann extension $A_{K,\\Omega,m}$ in $L^2(\\Omega)$. With $N(\\lambda,A_{K,\\Omega,m})$, $\\lambda > 0$, denoting the eigenvalue counting function corresponding to the strictly positive eigenvalues of $A_{K,\\Omega,m}$, we derive the bound $$ N(\\lambda,A_{K,\\Omega,m}) \\leq (2 \\pi)^{-n} v_n |\\Omega| \\{1 + [2m/(2m+n)]\\}^{n/(2m)} \\lambda^{n/(2m)}, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3731","kind":"arxiv","version":4},"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"}