{"paper":{"title":"Bohr's phenomenon for functions on the Boolean cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andreas Defant, Antonio P\\'erez, Mieczys{\\l}aw Masty{\\l}o","submitted_at":"2017-07-28T11:03:55Z","abstract_excerpt":"We study the asymptotic decay of the Fourier spectrum of real functions $f\\colon \\{-1,1\\}^N \\rightarrow \\mathbb{R}$ in the spirit of Bohr's phenomenon from complex analysis. Every such function admits a canonical representation through its Fourier-Walsh expansion $f(x) = \\sum_{S\\subset \\{1,\\ldots,N\\}}\\widehat{f}(S) x^S \\,,$ where $x^S = \\prod_{k \\in S} x_k$. Given a class $\\mathcal{F}$ of functions on the Boolean cube $\\{-1, 1\\}^{N} $, the Boolean radius of $\\mathcal{F}$ is defined to be the largest $\\rho \\geq 0$ such that $\\sum_{S}{|\\widehat{f}(S)| \\rho^{|S|}} \\leq \\|f\\|_{\\infty}$ for every $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09186","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"}