{"paper":{"title":"Functions with isotropic sections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Christos Saroglou, Ioannis Purnaras","submitted_at":"2019-06-25T10:30:07Z","abstract_excerpt":"We prove a local version of a recently established theorem by Myroshnychenko, Ryabogin and the second named author. More specifically, we show that if $n\\geq 3$, $g:\\mathbb{S}^{n-1}\\to\\mathbb{R}$ is an even bounded measurable function, $U$ is an open subset of $\\mathbb{S}^{n-1}$ and the restriction (section) of $f$ onto any great sphere perpendicular to $U$ is isotropic, then ${\\cal C}(g)|_U=c+\\langle a,\\cdot\\rangle$ and ${\\cal R}(g)|_U=c'$, for some fixed constants $c,c'\\in\\mathbb{R}$ and for some fixed vector $a\\in \\mathbb{R}^n$. Here, ${\\cal C}(g)$ denotes the cosine transform and ${\\cal R}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10439","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"}