{"paper":{"title":"Nikishin systems on the unit circle","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.CA","authors_text":"Rostyslav Kozhan","submitted_at":"2024-10-28T08:02:20Z","abstract_excerpt":"We introduce Nikishin system of $r$ probability measures on the unit circle. We show that such systems satisfy the AT property and therefore normality, introduced in~\\cite{KVMLOPUC}, for any multi-index $(n_1,\\ldots,n_r)\\in\\mathbb{N}^r$ with same-parity components satisfying $n_1 \\ge n_2 \\ge\\ldots\\ge n_r$. In the case of $r=2$, we demonstrate that the same property holds without requiring $n_1 \\ge n_2 \\ge\\ldots\\ge n_r$.\n  The analogous simple proof works for Nikishin systems on the real line for indices satisfying $n_j\\ge \\max\\{n_{j+1},\\ldots,n_r\\}-1$, $j=1,\\ldots,r-1$. This is related to the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.20813","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.20813/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}