Abstract shearlet transform
type: Item
instance of: scholarly article
title: Abstract shearlet transform
zbMATH Open document ID: 1333.42054
author: V. Atayi
author: R. A. Kamyabi-Gol
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2016-02-03T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1447856066
review text: Approximately ten years ago the generalization of wavelets to shearlets started its development. This paper extends shearlets (introduced in 2005 to find efficient extensions for the classical wavelet transform, see among others \textit{G. Kutyniok} and \textit{D. Labate} [``Construction of regular and irregular shearlet frames'', J. Wavelet Theory Appl. 1, No. 1, 1--12 (2007)] from Euclidean spaces to locally compact groups. The layout of the paper is as follows: \S1. { Introduction} \quad Gives an overview of the developments. \S2. { Preliminaries and notations} \quad Introducing the semidirect product \(G=H\times_{\tau}K\) of locally compact groups (\(h\mapsto \tau_h\) being a homeomorphism of \(H\) into the group \(\Aut(K)\) of automorphisms of \(K\); \((h,k)\mapsto \tau_h(k)\) from \(H\times K\) into \(K\) assumed continuous) and the left Haar measure on \(G\). \S3. { Main results} \quad Here, three locally compact groups play a role and the results are given in Theorems 3.4, 3.5 and 3.9. \S4. { Examples} \quad In this section, six different examples are given. \hskip0.6cm { References} \quad Contains 20 items (18 of which date from years after 2004).
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 43A65
zbMATH DE Number: 6538896
zbMATH Keywords: shearlet group
zbMATH Keywords: shearlet transform
zbMATH Keywords: semidirect product
zbMATH Keywords: quasiregular representation
reviewed by: Marcel G. de Bruin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6538896