{"paper":{"title":"An Improvement to a Berezin-Li-Yau type inequality for the Klein-Gordon Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Selma Yildirim Yolcu","submitted_at":"2009-09-23T06:37:04Z","abstract_excerpt":"In this article we improve a lower bound for $\\sum_{j=1}^k\\beta_j$ (a Berezin-Li-Yau type inequality) in [E. M. Harrell II and S. Yildirim Yolcu, Eigenvalue inequalities for Klein-Gordon Operators, J. Funct. Analysis, 256(12) (2009) 3977-3995]. Here $\\beta_j$ denotes the $j$th eigenvalue of the Klein Gordon Hamiltonian $H_{0,\\Omega}=|p|$ when restricted to a bounded set $\\Omega\\subset {\\mathbb R}^n$. $H_{0,\\Omega}$ can also be described as the generator of the Cauchy stochastic process with a killing condition on $\\partial \\Omega$. (cf. [R. Banuelos, T. Kulczycki, Eigenvalue gaps for the Cauch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.4132","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"}