{"paper":{"title":"A bound for the eigenvalue counting function for Krein--von Neumann and Friedrichs extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.AP","authors_text":"Ari Laptev, Fritz Gesztesy, Marius Mitrea, Mark S. Ashbaugh, Selim Sukhtaiev","submitted_at":"2016-05-04T07:40:32Z","abstract_excerpt":"For an arbitrary open, nonempty, bounded set $\\Omega \\subset \\mathbb{R}^n$, $n \\in \\mathbb{N}$, and sufficiently smooth coefficients $a,b,q$, we consider the closed, strictly positive, higher-order differential operator $A_{\\Omega, 2m} (a,b,q)$ in $L^2(\\Omega)$ defined on $W_0^{2m,2}(\\Omega)$, associated with the higher-order differential expression $$ \\tau_{2m} (a,b,q) := \\bigg(\\sum_{j,k=1}^{n} (-i \\partial_j - b_j) a_{j,k} (-i \\partial_k - b_k)+q\\bigg)^m, \\quad m \\in \\mathbb{N}, $$ and its Krein--von Neumann extension $A_{K, \\Omega, 2m} (a,b,q)$ in $L^2(\\Omega)$. Denoting by $N(\\lambda; A_{K"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01170","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"}