{"paper":{"title":"Radon Transforms for Mutually Orthogonal Affine Planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Boris Rubin, Yingzhan Wang","submitted_at":"2019-01-04T14:46:51Z","abstract_excerpt":"We study a Radon-like transform that takes functions on the Grassmannian of $j$-dimensional affine planes in $\\Bbb R ^n$ to functions on a similar manifold of $k$-dimensional planes by integration over the set of all $j$-planes that meet a given $k$-plane at a right angle. The case $j=0$ gives the classical Radon-John $k$-plane transform. For any $j$ and $k$, our transform has a mixed structure combining the $k$-plane transform and the dual $j$-plane transform. The main results include action of such transforms on rotation invariant functions, sharp existence conditions, intertwining propertie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01150","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"}