Funk, Cosine, and Sine Transforms on Stiefel and Grassmann Manifolds

The Funk, cosine, and sine transforms on the unit sphere are indispensable tools in integral geometry and related harmonic analysis. The aim of this 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 homogeneous distributions, analytic continuation, inversion formulas, and some applications.