2 citations · 2 across the 5 of their papers we have counts for
5 papers
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…
The shifted Wave equation on non flat harmonic manifolds
Oliver Brammen
We solve the shifted wave equation \begin{align*} \frac{\partial^2}{\partial t^2}φ(x,t)=(Δ_x+ρ^2)φ(x,t) \end{align*} on a non compact simply connected harmonic manifold with mean c…