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Mediterranean Journal of Mathematics

, Volume 6, Issue 3, pp 303–316 | Cite as

Integral Geometry on Discrete Grassmannians in Z n

  • Ahmed Abouelaz
  • Enrico Casadio Tarabusi
  • Abdallah Ihsane
Article

Abstract

We study the Radon transform R on the discrete Grassmannian of rank-d affine sublattices of Z n for 0 <  dn, extending and building on previous work of the first- and third-named authors in codimension 1. By analogy with the integral geometry on Grassmannians in R n , various natural questions are treated, such as definition and properties of R and its dual transform R *, function space setting, support theorems and inversion formulas.

Mathematics Subject Classification (2000)

Primary 44A12 Secondary 05B35 11D04 

Keywords

Radon transform dual Radon transform group actions Fourier transform systems of linear Diophantine equations sublattices Smith normal form 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Ahmed Abouelaz
    • 1
  • Enrico Casadio Tarabusi
    • 2
  • Abdallah Ihsane
    • 1
  1. 1.Département de Mathématiques et InformatiqueUniversité Hassan II Casablanca, Faculté des Sciences Aïn ChockCasablancaMorocco
  2. 2.Dipartimento di Matematica “G. Castelnuovo”Sapienza Università di RomaRomaItaly

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