{"paper":{"title":"Radon transform on real, complex and quaternionic Grassmannians","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Genkai Zhang","submitted_at":"2006-10-30T13:00:55Z","abstract_excerpt":"Let $G_{n,k}(\\bbK)$ be the\n Grassmannian manifold of $k$-dimensional $\\bbK$-subspaces in $\\bbK^n$ where $\\bbK=\\mathbb R, \\mathbb C, \\mathbb H$ is the field of real, complex or quaternionic numbers.\n For $1\\le k < k^\\prime \\le n-1$ we define the Radon transform $(\\mathcal R f)(\\eta)$, $\\eta \\in G_{n,k^\\prime}(\\bbK)$, for functions $f(\\xi)$ on $G_{n,k}(\\bbK)$ as an integration over all $\\xi \\subset \\eta$. When $k+k^\\prime \\le n$ we give an inversion formula in terms of the G\\aa{}rding-Gindikin fractional integration and the Cayley type differential operator on the symmetric cone of positive $k\\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610927","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"}