An abstract $L^2$ Fourier restriction theorem

Jonathan Hickman, James Wright

Type: Article

Publication Date: 2019-01-01

Citations: 4

DOI: https://doi.org/10.4310/mrl.2019.v26.n1.a6

Abstract

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 Z/N Z.

Locations

Mathematical Research Letters - View
arXiv (Cornell University) - View - PDF
Edinburgh Research Explorer (University of Edinburgh) - View - PDF

Similar Works

Action	Title	Year	Authors
+	An abstract $L^2$ Fourier restriction theorem	2018	Jonathan Hickman James Wright
+	An abstract $L^2$ Fourier restriction theorem	2018	Jonathan E. Hickman James Wright
+	Fourier restriction phenomenon in thin sets	2010	C. Papadimitropoulos
+	Fourier restriction estimates	2021	Valentina Ciccone
+ PDF Chat	Improved Fourier restriction estimates in higher dimensions	2019	Jonathan Hickman Keith M. Rogers
+	Improved Fourier restriction estimates in higher dimensions	2018	Jonathan E. Hickman Keith M. Rogers
+	Improved Fourier restriction estimates in higher dimensions	2018	Jonathan Hickman Keith M. Rogers
+ PDF Chat	Discrete restriction estimates for forms in many variables	2023	Brian Cook Kevin Hughes Eyvindur A. Palsson
+	Fourier restriction estimates for surfaces of co-dimension two in $\mathbb{R}^5$	2020	Shaoming Guo Changkeun Oh
+	Salem sets in local fields, the Fourier restriction phenomenon and the Hausdorff–Young inequality	2010	C. Papadimitropoulos
+	Picard groups in $p$-adic Fourier theory	2009	Tobias Schmidt
+	Picard groups in $p$-adic Fourier theory	2009	Tobias Schmidt
+	A note on Fourier restriction and nested Polynomial Wolff axioms	2020	Jonathan E. Hickman Joshua Zahl
+	Fourier Analysis on Locally Compact Abelian Groups	2004	Yitzhak Katznelson
+	Uniform estimates for Fourier restriction to polynomial curves in $\mathbb R^d$	2017	Betsy Stovall
+	Uniform estimates for Fourier restriction to polynomial curves in $\mathbb R^d$	2017	Betsy Stovall
+	A Freiman-type theorem for locally compact abelian groups	2007	Tom Sanders
+	Salem Sets in the p-adics, the Fourier Restriction Phenomenon and Optimal Extension of the Hausdorff-Young Inequality	2009	C. Papadimitropoulos
+ PDF Chat	On Farrell-Tate cohomology of SL_2 over S-integers	2014	Alexander Rahm Matthias Wendt
+	On Farrell-Tate cohomology of SL\_2 over S-integers	2014	Alexander Rahm Matthias Wendt

Works That Cite This (4)

Action	Title	Year	Authors
+ PDF Chat	Averages and maximal averages over Product j-varieties in finite fields	2021	Doowon Koh Sujin Lee
+ PDF Chat	The Fourier restriction and Kakeya problems over rings of integers modulo N	2018	Jonathan Hickman James Wright
+	Counting factorisations of monomials over rings of integers modulo $N$	2017	Jonathan Hickman James Wright
+ PDF Chat	Counting factorisations of monomials over rings of integers modulo N	2019	Jonathan Hickman James Wright

Works Cited by This (33)

Action	Title	Year	Authors
+	Fourier Analysis on Local Fields.	2016	Mitchell Taibleson
+	Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals	2002	Elias M. Stein Timothy S Murphy
+ PDF Chat	On the restriction of the Fourier transform to curves: endpoint results and the degenerate case	1985	Michael Christ
+	On the size of Kakeya sets in finite fields	2008	Zeev Dvir
+	Endpoint restriction estimates for the paraboloid over finite fields	2011	Allison Lewko Mark Lewko
+ PDF Chat	Restriction and Kakeya phenomena for finite fields	2004	Gerd Mockenhaupt Terence Tao
+	Salem sets and restriction properties of Fourier transforms	2000	Gerd Mockenhaupt
+ PDF Chat	On Fourier restriction and the Newton polygon	2008	Ákos Magyar
+ PDF Chat	Extension theorems for paraboloids in the finite field setting	2009	Alex Iosevich Doowon Koh
+ PDF Chat	A restriction theorem for the Fourier transform	1975	Peter A. Tomas