Spectral concentration of positive functions on compact groups
type: Item
instance of: scholarly article
title: Spectral concentration of positive functions on compact groups
zbMATH Open document ID: 1230.42033
author: Gorjan Alagic
author: Alexander Russell
published in: The Journal of Fourier Analysis and Applications
publication date: 2011-10-11T00:00:00Z
review text: It is well known that quadrature rules are basic tools for numerical integration and can be related in a variety of settings. The authors only require that the quadrature rules have positive weights and they prefer rules with small simple sets. The focus of the paper is to give a probabilistic (nonconstructive) proof for the existence of quadrature rules that apply to any band limit on any compact group. The authors construct new quadrature rules and prove lower bands on their maximum weights. Finally, these rules are applied to prove a spectral concentration theorem for band-limited positive functions (this is the main result of the paper).
Mathematics Subject Classification ID: 42B99
zbMATH DE Number: 5956251
zbMATH Keywords: approximation
zbMATH Keywords: positive functions
zbMATH Keywords: band limited functions
zbMATH Keywords: spectral analysis
reviewed by: Dan Bărbosu
MaRDI profile type: Publication
full work available at URL: s00041-011-9174-5
OpenAlex ID: W2051491283
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DOI: 10.1007/S00041-011-9174-5
description: scientific article; zbMATH DE number 5956251