{"paper":{"title":"Gabor unconditional bases and frames in $L^p(\\mathbb{R})$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Anton Tselishchev, Nir Lev","submitted_at":"2026-05-18T07:27:44Z","abstract_excerpt":"We consider the following problem: given a set $\\Lambda \\subset \\mathbb{R} \\times \\mathbb{R}$ and $p \\neq 2$, does there exist a function $g \\in L^p(\\mathbb{R})$ such that the Gabor system $\\{g(x-t) e^{2 \\pi isx}\\}$, $(t,s) \\in \\Lambda$, consisting of time-frequency shifts of $g$, forms an unconditional basis or unconditional Schauder frame in the space $L^p(\\mathbb{R})$? We completely resolve this question for $p>2$; in particular, we characterize the sets $\\Lambda$ such that an unconditional Schauder frame of this form exists. We also prove a Balian-Low type result, showing that the window f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17970","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/2605.17970/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.576247Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"8b945d8a04f7c4cd8bc1d871e1656b47a0ba2b30fe47f32421e5b9382e9cb70f"},"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"}