TY - JOUR
T1 - Dual radon transforms on affine grassmann manifolds
AU - Gonzalez, Fulton B.
AU - Kakehi, Tomoyuki
N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2004/10
Y1 - 2004/10
N2 - 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.
AB - 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.
KW - Grassmannian
KW - Pfaffian systems
KW - Radon transform
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U2 - 10.1090/S0002-9947-04-03471-3
DO - 10.1090/S0002-9947-04-03471-3
M3 - Article
AN - SCOPUS:4644223340
VL - 356
SP - 4161
EP - 4180
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 10
ER -