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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0610927","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"2006-10-30T13:00:55Z","cross_cats_sorted":[],"title_canon_sha256":"11e27e568a42130969aff107005188c52f1cc7b0b22be01f5e5d89589d4fe85b","abstract_canon_sha256":"59cae966615690f64c7ecff98f08738b81f1089409f54dfe751ada8787e2a765"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:22.524111Z","signature_b64":"FGID9Eyu5RjJ4AZlcOGadlYSgPZmjO8JbelTv3O6BhIrgJt45tqYzrlbZWn56rFlvopehfDZSCrp21QAK+5uBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2db52b01b13a3d5fa1e15fd913259decf164c2de1779cc56c9d0ffa2020ee915","last_reissued_at":"2026-05-18T01:05:22.523418Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:22.523418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\xi \\subset \\eta$. 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