{"paper":{"title":"The Fourier transform of multiradial functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Frederic Bernicot (LMJL), Loukas Grafakos (MU Mathematics), Yandan Zhang","submitted_at":"2013-07-31T18:06:10Z","abstract_excerpt":"We obtain an exact formula for the Fourier transform of multiradial functions, i.e., functions of the form $\\Phi(x)=\\phi(|x_1|, \\dots, |x_m|)$, $x_i\\in \\mathbf R^{n_i}$, in terms of the Fourier transform of the function $\\phi$ on $\\mathbf R^{r_1}\\times \\cdots \\times \\mathbf R^{r_m}$, where $r_i$ is either 1 or 2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.8408","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"}