{"paper":{"title":"Trigonometric bases in noncommutative $L_p(\\mathbb{T}^d_\\theta)$ spaces and associated partial sum operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"B. Ozbekbay, F. Sukochev, K. Tulenov","submitted_at":"2026-06-03T04:22:45Z","abstract_excerpt":"We develop a harmonic-analytic method for constructing a generalized trigonometric system in noncommutative $L_p(\\mathbb{T}^d_\\theta)$ spaces arising from the strongly continuous representation of $\\mathbb{T}^d$ and show that the generalized trigonometric system is a Schauder basis in $L_p(\\mathbb{T}^d_\\theta)$ for $1<p<\\infty.$ In particular, we prove that this trigonometric system forms an RUC-basis in $L_p(\\mathbb{T}^d_\\theta)$ for $2<p<\\infty.$ Our results provide a noncommutative counterpart of the classical trigonometric basis in $L_p(\\mathbb{T}^d)$. Further, we obtain a weak $(1,1)$ typ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19360","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/2606.19360/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"}