{"paper":{"title":"Pointwise characteristic factors for Wiener Wintner double recurrence theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"David Duncan, Idris Assani, Ryo Moore","submitted_at":"2014-02-27T21:40:36Z","abstract_excerpt":"In this paper, we extend Bourgain's double recurrence result to the Wiener-Wintner averages. Let $(X, \\mathcal{F}, \\mu, T)$ be a standard ergodic system. We will show that for any $f_1, f_2 \\in L^\\infty(X)$, the double recurrence Wiener-Wintner average\n  \\[ \\frac{1}{N} \\sum_{n=1}^N f_1(T^{an}x)f_2(T^{bn}x) e^{2\\pi i n t} \\] converges off a single null set of $X$ independent of $t$ as $N \\to \\infty$. Furthermore, we will show a uniform Wiener-Wintner double recurrence result: If either $f_1$ or $f_2$ belongs to the orthogonal complement of the Conze-Lesigne factor, then there exists a set of fu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.7094","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"}