{"paper":{"title":"On transfer operators on the circle with trigonometric weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.NT"],"primary_cat":"math.DS","authors_text":"Hans Volkmer, Xianghong Chen","submitted_at":"2016-10-24T21:38:03Z","abstract_excerpt":"We study spectral properties of the transfer operators $L$ defined on the circle $\\mathbb T=\\mathbb R/\\mathbb Z$ by $$(Lu)(t)=\\frac{1}{d}\\sum_{i=0}^{d-1} f\\left(\\frac{t+i}{d}\\right)u\\left(\\frac{t+i}{d}\\right),\\ t\\in\\mathbb T$$ where $u$ is a function on $\\mathbb T$. We focus in particular on the cases $f(t)=|\\cos(\\pi t)|^q$ and $f(t)=|\\sin(\\pi t)|^q$, which are closely related to some classical Fourier-analytic questions. We also obtain some explicit computations, particularly in the case $d=2$. Our study extends work of Strichartz \\cite{Strichartz1990} and Fan and Lau \\cite{FanLau1998}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07658","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":""},"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"}