{"paper":{"title":"Inverse of Infinite Hankel Moment Matrices","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Christian Berg, Ryszard Szwarc","submitted_at":"2018-01-18T13:49:02Z","abstract_excerpt":"Let $(s_n)_{n\\ge 0}$ denote an indeterminate Hamburger moment sequence and let $\\mathcal H=\\{s_{m+n}\\}$ be the corresponding positive definite Hankel matrix. We consider the question if there exists an infinite symmetric matrix $\\mathcal A=\\{a_{j,k}\\}$, which is an inverse of $\\mathcal H$ in the sense that the matrix product $\\mathcal A\\mathcal H$ is defined by absolutely convergent series and $\\mathcal A\\mathcal H$ equals the identity matrix $\\mathcal I$, a property called (aci). A candidate for $\\mathcal A$ is the coefficient matrix of the reproducing kernel of the moment problem, considered"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06013","kind":"arxiv","version":2},"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"}