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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Dual Radon transforms on affine Grassmann manifolds
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by Fulton B. Gonzalez and Tomoyuki Kakehi PDF
Trans. Amer. Math. Soc. 356 (2004), 4161-4180 Request permission

Abstract:

Fix $0 \leq p < q \leq n-1$, and let $G(p,n)$ and $G(q,n)$ denote the affine Grassmann manifolds of $p$- and $q$-planes in $\mathbb {R}^n$. We investigate the Radon transform $\mathcal {R}^{(q,p)} : C^{\infty } (G(q,n)) \to C^{\infty } (G(p,n))$ 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 $p+q =n$.
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Additional Information
  • Fulton B. Gonzalez
  • Affiliation: Department of Mathematics, Tufts University, Medford, Massachusetts 02155-7049
  • Email: fulton.gonzalez@tufts.edu
  • Tomoyuki Kakehi
  • Affiliation: Institute of Mathematics, University of Tsukuba, Ibaraki, Japan 305-8571
  • Email: kakehi@math.tsukuba.ac.jp
  • Received by editor(s): November 26, 2002
  • Received by editor(s) in revised form: May 1, 2003, and July 17, 2003
  • Published electronically: April 16, 2004
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 4161-4180
  • MSC (2000): Primary 44A12; Secondary 43A85
  • DOI: https://doi.org/10.1090/S0002-9947-04-03471-3
  • MathSciNet review: 2058842