Uncertainty Principles on Harmonic Manifolds of Rank One

Abstract

We show various uncertainty principles for the Fourier transform on harmonic manifolds of rank one. In particular, we derive a Heisenberg uncertainty principle, a Morgen theorem, an uncertainty principle for the Schr\"odinger equation and a version of H\"omanders theorem. Furthermore, we generalise the in the Euclidean case well-known Hausdorff-Young inequality for the Fourier transform, to harmonic manifolds of rank one.