Continuous wavelet transforms with applications to analyzing functions on spheres
type: Item
instance of: scholarly article
title: Continuous wavelet transforms with applications to analyzing functions on spheres
zbMATH Open document ID: 0902.42017
author: Stephan Dahlke
author: Peter Maass
published in: The Journal of Fourier Analysis and Applications
publication date: 1998-05-14T00:00:00Z
full work available at URL: https://eudml.org/doc/59485
review text: The paper provides a generalized continuous wavelet transform for \(L^2\)-spaces on a compact manifold \(M\). The generalized translation can be defined as the transitive action of a Lie group \(G\) on \(M\). However, the scaling process does not fit together with the topological structure of the manifold. Therefore one works with the tangent bundle \(TM\) of \(M\). Then the scaling process can be performed in the (noncompact) fibers. The idea is worked out for \(TS^1\) and \(TS^2\). The paper follows the general construction of wavelet transforms by \textit{A. Grossmann, J. Morlet} and \textit{T. Paul} [J. Math. Phys. 26, 2473-2479 (1985; Zbl 0571.22021)], looking for groups with square-integrable representations in \(L^2(TS^1)\) or \(L^2(TS^2)\). Applications of this construction for analyzing functions on \(S^1\) and \(S^2\) are presented.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 22D10
Mathematics Subject Classification ID: 55R25
Mathematics Subject Classification ID: 57S25
zbMATH DE Number: 1153111
zbMATH Keywords: wavelet transform
zbMATH Keywords: square-integrable representations
zbMATH Keywords: tangent bundles
zbMATH Keywords: homogeneous spaces
reviewed by: Gerlind Plonka
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1153111