### 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 |

Externally published | Yes |

### Fingerprint

### Keywords

- Grassmannian
- Moment condition
- Radon transform
- Support theorem

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Advances in Mathematics*,

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

**Moment conditions and support theorems for Radon transforms on affine Grassmann manifolds.** / Gonzalez, Fulton B.; Kakehi, Tomoyuki.

Research output: Contribution to journal › Article

*Advances in Mathematics*, vol. 201, no. 2, pp. 516-548. https://doi.org/10.1016/j.aim.2005.02.009

}

TY - JOUR

T1 - Moment conditions and support theorems for Radon transforms on affine Grassmann manifolds

AU - Gonzalez, Fulton B.

AU - Kakehi, Tomoyuki

PY - 2006/4/1

Y1 - 2006/4/1

N2 - Let G(p, n) and G(q, n) be the affine Grassmann manifolds of p- and q-planes in ℝn, 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 (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)

AB - Let G(p, n) and G(q, n) be the affine Grassmann manifolds of p- and q-planes in ℝn, 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 (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)

KW - Grassmannian

KW - Moment condition

KW - Radon transform

KW - Support theorem

UR - http://www.scopus.com/inward/record.url?scp=33644849473&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33644849473&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2005.02.009

DO - 10.1016/j.aim.2005.02.009

M3 - Article

AN - SCOPUS:33644849473

VL - 201

SP - 516

EP - 548

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 2

ER -