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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)}, "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1403.3731","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-03-15T00:35:17Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"96fe4cffa5aa21147d81ce884457f8c5bea2deff33e3f5ae29d5a486cdd54672","abstract_canon_sha256":"cf3a0351b443192ae4dc22192a576dc3dc64dd417f8caa854b537a68cd48f7d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:12.724759Z","signature_b64":"RJt0SgbSU9DCbD9ivpDe0bCiTYx1oxC8tkh1Hrx9CarN6WJHQt/hrcOScHjVBcEu3WHMRHBdayO0ynANhMpxDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6e63d27af40cb9dbaa21ca6eb83bf3cc5838fd12451c82d69ef1202d305acd6","last_reissued_at":"2026-05-18T02:50:12.724096Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:12.724096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $L^2(\\Omega)$. 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