A remark on the Schrödinger equation on Zoll manifolds

Abstract

On the one dimensional sphere, the support of the fundamental solution to the Schr$\ddot{\mathrm{o}}$dinger equation consists of finite points at the time $t\in 2π\Q$. The paper \cite{Ka} generalized this fact to compact symmetric spaces. In this paper, we consider similar results on Zoll manifolds. We study the singularity for a solution to the equation using a functional calculus of the self-adjoint operator with integer eigenvalues.

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