{"paper":{"title":"On Sets of Large Fourier Transform Under Changes in Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Barak Shani, Joel Laity","submitted_at":"2016-10-14T04:44:49Z","abstract_excerpt":"A function $f:\\mathbb{Z}_n \\to \\mathbb{C}$ can be represented as a linear combination $f(x)=\\sum_{\\alpha \\in \\mathbb{Z}_n}\\widehat{f}(\\alpha) \\chi_{\\alpha,n}(x)$ where $\\widehat{f}$ is the (discrete) Fourier transform of $f$. Clearly, the basis $\\{\\chi_{\\alpha,n}(x):=\\exp(2\\pi i \\alpha x/n)\\}$ depends on the value $n$.\n  We show that if $f$ has \"large\" Fourier coefficients, then the function $\\widetilde{f}:\\mathbb{Z}_m \\to \\mathbb{C}$, given by \\[\n  \\widetilde{f}(x)\n  = \\begin{cases} f(x) & \\text{when } 0\\leq x < \\min(n, m),\n  0 & \\text{otherwise},\n  \\end{cases} \\] also has \"large\" coefficient"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04330","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"}