Integral geometry on Grassmann manifolds and calculus of invariant differential operators

Tomoyuki Kakehi

Research output: Contribution to journalArticle

16 Citations (Scopus)


In this paper, we mainly deal with two problems in integral geometry, the range characterizations and construction of inversion formulas for Radon transforms on higher rank Grassmann manifolds. The results will be described explicitly in terms of invariant differential operators. We will also study the harmonic analysis on Grassmann manifolds, using the method of integral geometry. In particular, we will give eigenvalue formulas and radial part formulas for invariant differential operators.

Original languageEnglish
Article numberjfan.1999.3459
Pages (from-to)1-45
Number of pages45
JournalJournal of Functional Analysis
Issue number1
Publication statusPublished - Jan 1 1999



  • Eigenvalue formula
  • Grassmann manifold
  • Integral geometry
  • Invariant differential operator
  • Inversion formula
  • Radial part
  • Radon transform
  • Range-characterization

ASJC Scopus subject areas

  • Analysis

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