Dual radon transforms on affine grassmann manifolds

Fulton B. Gonzalez; Tomoyuki Kakehi

doi:10.1090/S0002-9947-04-03471-3

Dual radon transforms on affine grassmann manifolds

Fulton B. Gonzalez, Tomoyuki Kakehi

Graduate School of Natural Science and Technology

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

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
Pages (from-to)	4161-4180
Number of pages	20
Journal	Transactions of the American Mathematical Society
Volume	356
Issue number	10
DOIs	https://doi.org/10.1090/S0002-9947-04-03471-3
Publication status	Published - Oct 2004

Keywords

Grassmannian
Pfaffian systems
Radon transform

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/S0002-9947-04-03471-3

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AU - Gonzalez, Fulton B.

AU - Kakehi, Tomoyuki

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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.

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