4 papers · 1 filter
Uncertainty Principles on Harmonic Manifolds of Rank One
Oliver Brammen
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, a…
Differential Operators on Non-compact Harmonic Manifolds
Oliver Brammen
We study the algebra of differential operators on non-compact simply connected harmonic manifolds and provide sufficient conditions for them to have a radial fundamental solution a…
The Brownian Motion on Harmonic Manifolds of Purely Exponential Volume Growth
Oliver Brammen
We show that Sullivan's method of constructing eigenfunctions of the Laplacian \cite{Sullivan1987RelatedAO} is applicable to non-compact simply connected harmonic manifolds of pure…
Dynamics of -Multiplier for on Harmonic Manifolds of Purely Exponential Volume Growth
Oliver Brammen
We study the dynamics of -multipliers on non-compact simply connected harmonic manifolds of purely exponential volume growth. These are linear operators on the -spaces wh…