{"paper":{"title":"On infinite Jacobi matrices with a trace class resolvent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Pavel Stovicek","submitted_at":"2019-04-30T12:48:47Z","abstract_excerpt":"Let $\\{\\hat{P}_{n}(x)\\}$ be an orthonormal polynomial sequence and denote by $\\{w_{n}(x)\\}$ the respective sequence of functions of the second kind. Suppose the Hamburger moment problem for $\\{\\hat{P}_{n}(x)\\}$ is determinate and denote by $J$ the corresponding Jacobi matrix operator on $\\ell^{2}$. We show that if $J$ is positive definite and $J^{-1}$ belongs to the trace class then the series on the right-hand side of the defining equation \\[ \\mathfrak{F}(z):=1-z\\sum_{n=0}^{\\infty}w_{n}(0)\\hat{P}_{n}(z) \\] converges locally uniformly on $\\mathbb{C}$ and it holds true that $\\mathfrak{F}(z)=\\pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.13199","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"}