### Abstract

Let G(p, n) and G(q, n) be the affine Grassmann manifolds of p- and q-planes in ℝ^{n}, respectively, and let ℛ^{(p,q)} be the Radon transform from smooth functions on G(p, n) to smooth functions on G(q, n) arising from the inclusion incidence relation. When p < q and dim G(p, n) = dim G(p, n), we present a range characterization theorem for ℛ^{(p,q)} via moment conditions. We then use this range result to prove a support theorem for ℛ^{(p,q)}. This complements a previous range characterization theorem for ℛ^{(p,q)} via differential equations when dim G(p, n) < dim G(p, n). We also present a support theorem in this latter case.

Original language | English |
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Pages (from-to) | 516-548 |

Number of pages | 33 |

Journal | Advances in Mathematics |

Volume | 201 |

Issue number | 2 |

DOIs | |

Publication status | Published - Apr 1 2006 |

### Keywords

- Grassmannian
- Moment condition
- Radon transform
- Support theorem

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Gonzalez, F. B., & Kakehi, T. (2006). Moment conditions and support theorems for Radon transforms on affine Grassmann manifolds.

*Advances in Mathematics*,*201*(2), 516-548. https://doi.org/10.1016/j.aim.2005.02.009