1. Radon Transform on a Harmonic Manifold
- Author
-
François Rouvière
- Subjects
Pure mathematics ,Radon transform ,010102 general mathematics ,Fourier inversion theorem ,Harmonic (mathematics) ,Mathematics::Geometric Topology ,01 natural sciences ,Inversion (discrete mathematics) ,Manifold ,Harmonic analysis ,symbols.namesake ,Differential geometry ,Fourier analysis ,0103 physical sciences ,symbols ,Mathematics::Differential Geometry ,010307 mathematical physics ,Geometry and Topology ,0101 mathematics ,Mathematics - Abstract
We extend to a large class of noncompact harmonic manifolds the inversion formulas for the Radon transform on horospheres in hyperbolic spaces or Damek–Ricci spaces. Horospheres are defined here as level hypersurfaces of Busemann functions. The proof uses harmonic analysis on the manifolds considered, developed in a recent paper by Biswas, Knieper and Peyerimhoff; we also give a concise proof of their Fourier inversion theorem for harmonic manifolds.
- Published
- 2020