  The Funk, cosine, and sine transforms on the unit sphere are indispensable
tools in integral geometry. They are also known to be interesting objects in
harmonic analysis. The aim of the paper is to extend basic facts about these
transforms to the more general context for Stiefel or Grassmann manifolds. The
main topics are composition formulas, the Fourier functional relations for the
corresponding homogeneous distributions, analytic continuation, and explicit
inversion formulas.
