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Generalizing a result of Roe [14], Strichartz proved in [16] that if a doubly infinite sequence {fk} of functions on $\mathbb R^n$ satisfies fk+1=Δfk and |fk(x)|≤M for all k=0,±1,±2,… and $x\in \mathbb R^n$, then Δf0(x)=−f0. Strichartz also showed that the result fails for hyperbolic 3-space. This negative result can indeed be extended to any Riemannian symmetric space of noncompact type. Taking t...

A Theorem of Roe and Strichartz for Riemannian Symmetric Spaces of Noncompact Type