{"paper":{"title":"On Helson matrices: moment problems, non-negativity, boundedness, and finite rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Alexander Pushnitski, Karl-Mikael Perfekt","submitted_at":"2016-11-11T16:40:54Z","abstract_excerpt":"We study Helson matrices (also known as multiplicative Hankel matrices), i.e. infinite matrices of the form $M(\\alpha) = \\{\\alpha(nm)\\}_{n,m=1}^\\infty$, where $\\alpha$ is a sequence of complex numbers. Helson matrices are considered as linear operators on $\\ell^2(\\mathbb{N})$. By interpreting Helson matrices as Hankel matrices in countably many variables we use the theory of multivariate moment problems to show that $M(\\alpha)$ is non-negative if and only if $\\alpha$ is the moment sequence of a measure $\\mu$ on $\\mathbb{R}^\\infty$, assuming that $\\alpha$ does not grow too fast. We then charact"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03772","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"}