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

Fulton B. Gonzalez, Tomoyuki Kakehi

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Abstract

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 < 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 languageEnglish
Pages (from-to)516-548
Number of pages33
JournalAdvances in Mathematics
Volume201
Issue number2
DOIs
Publication statusPublished - Apr 1 2006

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Keywords

  • Grassmannian
  • Moment condition
  • Radon transform
  • Support theorem

ASJC Scopus subject areas

  • Mathematics(all)

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