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2020 Strichartz estimates for the Schrödinger flow on compact Lie groups
Yunfeng Zhang
Anal. PDE 13(4): 1173-1219 (2020). DOI: 10.2140/apde.2020.13.1173

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.

Citation

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Yunfeng Zhang. "Strichartz estimates for the Schrödinger flow on compact Lie groups." Anal. PDE 13 (4) 1173 - 1219, 2020. https://doi.org/10.2140/apde.2020.13.1173

Information

Received: 27 August 2018; Revised: 19 February 2019; Accepted: 18 April 2019; Published: 2020
First available in Project Euclid: 25 June 2020

zbMATH: 07221201
MathSciNet: MR4109904
Digital Object Identifier: 10.2140/apde.2020.13.1173

Subjects:
Primary: 42B37
Secondary: 22E30

Rights: Copyright © 2020 Mathematical Sciences Publishers

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