Mathematical Research Letters

Volume 26 (2019)

Number 1

An abstract $L^2$ Fourier restriction theorem

Pages: 75 – 100



Jonathan Hickman (Department of Mathematics, University of Chicago, Illinois, U.S.A.; and School of Mathematics and Statistics, Mathematical Institute, University of St Andrews, Fife, Scotland, United Kingdom)

James Wright (School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Scotland, United Kingdom)


An $L^2$ Fourier restriction argument of Bak and Seeger is abstracted to the setting of locally compact abelian groups. This is used to prove new restriction estimates for varieties lying in modules over local fields or rings of integers $\mathbb{Z} / N \mathbb{Z}$.

This material is based upon work supported by the National Science Foundation under Grant No. DMS-1440140 whilst the first author was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2017 semester.

Received 23 August 2017

Accepted 17 May 2018

Published 7 June 2019