A remark on the Schr\"odinger equation on Zoll manifolds

Hisashi Nishiyama

A remark on the Schr\"odinger equation on Zoll manifolds

Analysis of PDEs 2011-03-29 v1

Authors: Hisashi Nishiyama

Abstract

On the one dimensional sphere, the support of the fundamental solution to the Schr $\rm \ddot o$ dinger equation consists of finite points at the time $t\in 2\pi\Q$ . 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.

Keywords

schrödinger equation zoll manifolds fundamental solution singularity functional calculus self-adjoint operator

Cite

@article{arxiv.1103.5210,
  title  = {A remark on the Schr\"odinger equation on Zoll manifolds},
  author = {Hisashi Nishiyama},
  journal= {arXiv preprint arXiv:1103.5210},
  year   = {2011}
}

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