Clifford-Hermite wavelets in Euclidean space
type: Item
instance of: scholarly article
title: Clifford-Hermite wavelets in Euclidean space
zbMATH Open document ID: 0961.42021
DOI: 10.1007/BF02511157
published in: The Journal of Fourier Analysis and Applications
publication date: 2001-05-06T00:00:00Z
full work available at URL: https://eudml.org/doc/59644
review text: The continuous wavelet transform analyzes the distribution of a function in both space and scale using a wavelet function phi. Many choices of phi are possible; one example is the Marr wavelets, obtained by applying some power of the Laplacian to a Gaussian. In this paper these wavelets are generalized to Clifford-valued wavelets by applying some power of the Dirac operator to the Gaussian, thus obtaining Gaussians weighted by Hermite polynomials. Just as the family of scaled Gaussians obey the heat equation, the scaled Clifford-valued wavelets also obey a certain PDE which is worked out explicitly.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 30G35
zbMATH DE Number: 1445613
zbMATH Keywords: wavelets
zbMATH Keywords: Gaussians
zbMATH Keywords: Clifford algebra
zbMATH Keywords: Hermite polynomials
author: F. Brackx
author: Frank Sommen
reviewed by: Terence Tao
MaRDI profile type: Publication
cites work: Q4365124
cites work: Directional wavelets revisited: Cauchy wavelets and symmetry detection in patterns
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cites work: Ten Lectures on Wavelets
cites work: Special functions in Clifford analysis and axial symmetry
cites work: Q4015640
description: scientific article; zbMATH DE number 1445613