Characterization of wave front sets by wavelet transforms
type: Item
instance of: scholarly article
title: Characterization of wave front sets by wavelet transforms
zbMATH Open document ID: 1122.46021
author: Mirjana Vuletić
author: Stevan Pilipović
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2007-04-13T00:00:00Z
review text: To consider wave front sets of tempered distributions, the authors place emphasis on Moritoh's wavelet transforms. In the first part of the paper, they elaborate the wavelet transform \(W_\psi\) and the wave front sets for the wavelet \(\psi\), but for dimensions \(n= 1,2,3,4\) or \(8\), improving some known results concerning the estimates of wave fronts. In Theorem 7, they prove: Let \(f\in S'(\mathbb{R}^n)\). Then \(WF_\psi(f)= WF(f)\), \(n= 1,2,3,4\) or \(8\), where \(WF\) is the wave front defined by Hörmander. In the second part, the authors generalize the definition of \(W_\psi\) transform and extend their results to dimensions \(n\in\mathbb{N}\), excluding some directions in the frequency domain.
Mathematics Subject Classification ID: 46F12
Mathematics Subject Classification ID: 43A32
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 5142589
zbMATH Keywords: wave front
zbMATH Keywords: wavelet transform
zbMATH Keywords: tempered distributions
reviewed by: B. Stanković
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1163775136
OpenAlex ID: W1976587572
cites work: On the parallelizability of the spheres
cites work: Ten Lectures on Wavelets
cites work: Q4327556
cites work: Q3135829
cites work: Wavelet transforms in Euclidean spaces -- their relation with wave front sets and Besov, Triebel-Lizorkin spaces
cites work: Q3971548
cites work: The wavelet transform of distributions
DOI: 10.2748/TMJ/1163775136
description: scientific article; zbMATH DE number 5142589