Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1441-1497 |
| Number of pages | 57 |
| Journal | Journal of Geometric Analysis |
| Volume | 23 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jul 2013 |
| Externally published | Yes |
Keywords
- Cosine transform
- Fourier analysis
- Funk transform
- Radon transform
- Sine transform