Uncertainty principles in harmonic analysis
type: Item
instance of: scholarly article
title: Uncertainty principles in harmonic analysis
zbMATH Open document ID: 0682.43005
DOI: 10.1016/0022-1236(89)90112-2
author: Robert S. Strichartz
published in: Journal of Functional Analysis
publication date: 1989-01-01T00:00:00Z
review text: Suppose E is a subset of \({\mathbb{R}}^ n\) of codimension one which is ``uniformly distributed''. It is shown that if \(f\in L^ 2({\mathbb{R}}^ n)\), \(\| f\|_ 2=1\), \(Var(f)<\infty\), and \(\int_{E}| \hat f(\sigma)|^ 2d\sigma \leq C_ 1\) (where \(d\sigma\) is surface measure) then \(Var(f)\geq C_ 2(E,C_ 1)\). ``Uniformly distributed'' sets include parallel hyperplanes and concentric spheres which are uniformly spaced. A computation with the sphere suggests similar results for compact Riemannian manifolds.
Mathematics Subject Classification ID: 43A15
Mathematics Subject Classification ID: 42A99
zbMATH DE Number: 4117185
zbMATH Keywords: uniformly distributed sets
zbMATH Keywords: uncertainty principle
zbMATH Keywords: Fourier transform
reviewed by: Michael G. Cowling
MaRDI profile type: Publication
full work available at URL: 0022-1236(89)90112-2
OpenAlex ID: W2024769997
cites work: Harmonic analysis as spectral theory of Laplacians
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description: scientific article; zbMATH DE number 4117185