{"paper":{"title":"Eigenvalue decay of operators on harmonic function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"Cho-Ho Chu, Oscar F. Bandtlow","submitted_at":"2009-03-05T13:42:48Z","abstract_excerpt":"Let $\\Omega$ be an open set in $\\R^d$ $(d > 1)$ and $h(\\Omega)$ the Fr\\'echet space of harmonic functions on $\\Omega$. Given a bounded linear operator\n  $L :h(\\Omega)\\to h(\\Omega)$, we show that its eigenvalues $\\lambda_n$, arranged in decreasing order and counting multiplicities, satisfy\n  $|\\lambda_n|\\leq K\\exp(-cn^{1/(d-1)})$, where $K$ and $c$ are two explicitly computable positive constants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.0865","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"}