The Schrödinger equation on spheres

Michael Taylor

Vol. 209 (2003), No. 1, 145–155

DOI: 10.2140/pjm.2003.209.145

Abstract

It is shown that the fundamental solution to the Schrödinger equation on a d-dimensional sphere has an explicit description at times that are rational multiples of π. This leads to sharp L^p estimates on the solution operator at those times. Analogous, though less explicit, results are obtained when spheres are replaced by Zoll manifolds, and when potentials are added.

Milestones

Received: 10 December 2001

Revised: 25 March 2002

Published: 1 March 2003