{"paper":{"title":"The spectral gap for transfer operators of torus extensions over expanding maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Huyi Hu, Jianyu Chen","submitted_at":"2015-03-08T00:59:15Z","abstract_excerpt":"We study the spectral gap for transfer operators of the skew product $F: \\mathbb{T}^d\\times \\mathbb{T}^\\ell\\to \\mathbb{T}^d\\times \\mathbb{T}^\\ell$ given by $F(x,y)=(Tx, y+\\tau(x) \\pmod{ \\mathbb{Z}^\\ell})$, where $T: \\mathbb{T}^d\\to \\mathbb{T}^d$ is a $C^\\infty$ uniformly expanding endomorphism, and the fiber map $\\tau: \\mathbb{T}^d\\to \\mathbb{R}^\\ell$ is a $C^\\infty$ map. We construct a Hilbert space $\\mathcal{W}^{-s}$ for any $s<0$, which contains all the H\\\"older functions of H\\\"older exponents $|s|$ on $ \\mathbb{T}^d\\times \\mathbb{T}^\\ell$. Applying the method of semiclassical analysis, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02232","kind":"arxiv","version":3},"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"}