{"paper":{"title":"On higher-order Szego theorems with a single critical point of arbitrary order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Milivoje Lukic","submitted_at":"2013-10-24T19:06:38Z","abstract_excerpt":"We prove the following higher-order Szego theorems: if a measure on the unit circle has absolutely continuous part $w(\\theta)$ and Verblunsky coefficients $\\alpha$ with square-summable variation, then for any positive integer $m$, $\\int (1-\\cos \\theta)^m \\log w(\\theta) d\\theta$ is finite if and only if $\\alpha \\in \\ell^{2m+2}$.\n  This is the first known equivalence result of this kind in the regime of very slow decay, i.e. with $\\ell^p$ conditions with arbitrarily large $p$. The usual difficulty of controlling higher-order sum rules is avoided by a new test sequence approach."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6712","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"}