{"paper":{"title":"Overdetermined Transforms in Integral Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Boris Rubin","submitted_at":"2013-11-29T19:54:55Z","abstract_excerpt":"A simple example of an $n$-dimensional admissible complex of planes is given for the overdetermined $k$-plane transform in $\\mathbb{R}^n$. For the corresponding restricted $k$-plane transform sharp existence conditions are obtained and explicit inversion formulas are discussed in the general context of $L^p$ functions. Similar questions are studied for overdetermined Radon type transforms on the sphere and the hyperbolic space. A theorem describing the range of the restricted $k$-plane transform on the space of rapidly decreasing smooth functions is proved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7678","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"}