### 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 1 2004 |

### Keywords

- Grassmannian
- Pfaffian systems
- Radon transform

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Gonzalez, F. B., & Kakehi, T. (2004). Dual radon transforms on affine grassmann manifolds.

*Transactions of the American Mathematical Society*,*356*(10), 4161-4180. https://doi.org/10.1090/S0002-9947-04-03471-3