Wavelet Transform on Compact Gelfand Pairs and Its Discretization

Using harmonic analysis on a compact Gelfand pair (G,K), we study the continuous wavelet analysis on the homogeneous space G/K. As example we give the wavelet associated with the K-biinvariant Poisson kernel on G. Next, using the previous results, we define and study three types of wavelet packets o...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 238; no. 1; pp. 234 - 258
Main Authors Mokni, K., Trimèche, K.
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 01.10.1999
Elsevier
Subjects
Abstract harmonic analysis
Exact sciences and technology
Functional analysis
Group theory
Group theory and generalizations
Mathematical analysis
Mathematics
Sciences and techniques of general use
Topological groups, lie groups
Fourier transformation
Compact group
K biinvariance
Gel'fand pair
Harmonic analysis
Invariance
Multiresolution analysis
Complex number
Scaling function
Poisson kernel
Irreducible representation
Convolution
Discretization
Vector space
Wavelet transformation
Hilbert space
Lie group
Spherical function
Gegenbauer polynomial
Ultraspherical polynomial
Square integrable function
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Summary:Using harmonic analysis on a compact Gelfand pair (G,K), we study the continuous wavelet analysis on the homogeneous space G/K. As example we give the wavelet associated with the K-biinvariant Poisson kernel on G. Next, using the previous results, we define and study three types of wavelet packets on G/K and the corresponding wavelet transforms. We prove for these transforms reconstruction formulas, and we describe the related multiresolution analysis.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.1999.6530