Vol. 13, No. 4, 2020

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Strichartz estimates for the Schrödinger flow on compact Lie groups

Yunfeng Zhang

Vol. 13 (2020), No. 4, 1173–1219
Abstract

We establish scale-invariant Strichartz estimates for the Schrödinger flow on any compact Lie group equipped with canonical rational metrics. In particular, full Strichartz estimates without loss for some nonrectangular tori are given. The highlights of this paper include estimates for some Weyl-type sums defined on rational lattices, different decompositions of the Schrödinger kernel that accommodate different positions of the variable inside the maximal torus relative to the cell walls, and an application of the BGG-Demazure operators or Harish-Chandra’s integral formula to the estimate of the difference between characters.

Keywords
compact Lie groups, Schrödinger equation, circle method, Strichartz estimates, BGG-Demazure operators, Harish-Chandra's integral formula
Mathematical Subject Classification 2010
Primary: 42B37
Secondary: 22E30
Milestones
Received: 27 August 2018
Revised: 19 February 2019
Accepted: 18 April 2019
Published: 13 June 2020
Authors
Yunfeng Zhang
Department of Mathematics
University of Connecticut
Storrs, CT
United States