The spectral radius of a multivariate sampling operator
type: Item
instance of: scholarly article
title: The spectral radius of a multivariate sampling operator
zbMATH Open document ID: 1073.47041
author: Peter Zizler
published in: Linear Algebra and its Applications
publication date: 2004-08-06T00:00:00Z
review text: The author provides an upper bound on the spectral radius of a multivariate sampling operator \(S_h(M):f(\theta) \to h(\theta)f(\theta M)\), where \(f\in L^2(I_s)\), \(s\) is a natural number, \(I_s=[0,2\pi )^s\), \(\theta \in I_s\), \(M\) is an \(s\times s\) matrix with integer entries and \(h\) is a complex valued multivariate trigonometric polynomial on \(I_s\).
reviewed by: Mirosława Zima
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 65T60
zbMATH DE Number: 2083525
zbMATH Keywords: scaling function
zbMATH Keywords: smoothness
zbMATH Keywords: multiplication operator
zbMATH Keywords: multivariate sampling operator
zbMATH Keywords: spectral radius
zbMATH Keywords: wavelet analysis
MaRDI profile type: Publication
full work available at URL: j.laa.2003.12.042
OpenAlex ID: W2050905056
cites work: Construction of multivariate biorthogonal wavelets with arbitrary vanishing moments
cites work: Ten Lectures on Wavelets
cites work: Spectra of slant Toeplitz operators with continuous symbols
cites work: Adjoints of slant Toeplitz operators
cites work: Properties of slant Toeplitz operators
cites work: Q4044675
cites work: ON INTEGRO-FUNCTIONAL OPERATORS WITH A SHIFT WHICH IS NOT ONE-TO-ONE
cites work: The Sobolev regularity of refinable functions
cites work: Energy Moments in Time and Frequency for Two-Scale Difference Equation Solutions and Wavelets
cites work: Spectra of subdivision operators
DOI: 10.1016/J.LAA.2003.12.042
description: scientific article; zbMATH DE number 2083525