{"paper":{"title":"A Helson matrix with explicit eigenvalue asymptotics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.SP","authors_text":"Alexander Pushnitski, Nazar Miheisi","submitted_at":"2017-09-19T10:08:57Z","abstract_excerpt":"A Helson matrix (also known as a multiplicative Hankel matrix) is an infinite matrix with entries $\\{a(jk)\\}$ for $j,k\\geq1$. Here the $(j,k)$'th term depends on the product $jk$. We study a self-adjoint Helson matrix for a particular sequence $a(j)=(\\sqrt{j}\\log j(\\log\\log j)^\\alpha))^{-1}$, $j\\geq 3$, where $\\alpha>0$, and prove that it is compact and that its eigenvalues obey the asymptotics $\\lambda_n\\sim\\varkappa(\\alpha)/n^\\alpha$ as $n\\to\\infty$, with an explicit constant $\\varkappa(\\alpha)$. We also establish some intermediate results (of an independent interest) which give a connection"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06326","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"}