Abstract
Fix 0 ≤ p < q ≤ n - 1, and let G(p, n) and G(q, n) denote the affine Grassmann manifolds of p- and q-planes in ℝ n. We investigate the Radon transform R (q,p) : C ∞(G(q, n)) → C ∞(G(p, n)) associated with the inclusion incidence relation. For the generic case dim G(q, n) < dim G(p, n) and p + q > n, we will show that the range of this transform is given by smooth functions on G(p, n) annihilated by a system of Pfaffian type differential operators. We also study aspects of the exceptional case p + q = n.
Original language | English |
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Pages (from-to) | 4161-4180 |
Number of pages | 20 |
Journal | Transactions of the American Mathematical Society |
Volume | 356 |
Issue number | 10 |
DOIs | |
Publication status | Published - Oct 2004 |
Externally published | Yes |
Keywords
- Grassmannian
- Pfaffian systems
- Radon transform
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics