Dual radon transforms on affine grassmann manifolds

Fulton B. Gonzalez, Tomoyuki Kakehi

Research output: Contribution to journalArticle

5 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 languageEnglish
Pages (from-to)4161-4180
Number of pages20
JournalTransactions of the American Mathematical Society
Volume356
Issue number10
DOIs
Publication statusPublished - Oct 1 2004

Keywords

  • Grassmannian
  • Pfaffian systems
  • Radon transform

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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