Wavelets on the 2-sphere: A group-theoretical approach
type: Item
instance of: scholarly article
title: Wavelets on the 2-sphere: A group-theoretical approach
zbMATH Open document ID: 0945.42023
published in: Applied and Computational Harmonic Analysis
publication date: 2000-10-04T00:00:00Z
review text: In this paper the authors derive a continuous wavelet transform on the 2-dimensional sphere \(S^2\) using the square integrable group representation theory. The targeted group is the Lorentz group \(SO_0(3,1)\). Since its representation is not square integrable, the theory is restricted on a subgroup, namely the product \(SO(3)\) (the motions, or rotations) and \(R^{+}_{*}\) (the local dilations, acting on tangent space and pulled-back through the stereographic projection). Next, a necessary condition for admissibility is obtained, and, in the Euclidean limit (i.e., the sphere radius going to infinity) it becomes the usual zero mean necessary condition.
reviewed by: Radu Balan
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 22D10
zbMATH DE Number: 1384041
zbMATH Keywords: continuous wavelet transform
zbMATH Keywords: square integrable group representation
zbMATH Keywords: Lorentz group
author: J. P. Antoine
author: P. Vandergheynst
MaRDI profile type: Publication
full work available at URL: acha.1999.0272
OpenAlex ID: W2096897625
cites work: COHERENT STATES AND THEIR GENERALIZATIONS: A MATHEMATICAL OVERVIEW
cites work: Image analysis with two-dimensional continuous wavelet transform
cites work: Wavelets on the n-sphere and related manifolds
cites work: Wavelets in Physics
cites work: Multiresolution analysis and wavelets onS2andS3
cites work: Continuous wavelet transforms with applications to analyzing functions on spheres
cites work: Painless nonorthogonal expansions
cites work: Ten Lectures on Wavelets
cites work: Q3344388
cites work: Q3311232
cites work: Combined spherical harmonic and wavelet expansion -- a future concept in earth's gravitational determination
cites work: Q4380354
cites work: Locally supported wavelets on manifolds with applications to the 2D sphere
cites work: Transforms associated to square integrable group representations. I. General results
cites work: Q3735961
cites work: Continuous wavelet transforms on the sphere
cites work: On the Contraction of Groups and Their Representations
cites work: Lie groups beyond an introduction
cites work: Q5569793
cites work: Contractions of representations of de Sitter groups
cites work: Nonstationary wavelets on the \(m\)-sphere for scattered data
cites work: Q3743524
cites work: Q4259936
cites work: Q5451962
cites work: Q3842589
cites work: Spherical Radon transform and related wavelet transforms
cites work: Contraction of Lie Groups
cites work: The lifting scheme: A custom-design construction of biorthogonal wavelets
cites work: Sur les représentations unitaires des groupes de Lorentz généralisés
DOI: 10.1006/ACHA.1999.0272
description: scientific article; zbMATH DE number 1384041