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Dual wavelets associated with nonuniform MRA
- Source :
- Tamkang Journal of Mathematics. 50:119-132
- Publication Year :
- 2018
- Publisher :
- Tamkang Journal of Mathematics, 2018.
-
Abstract
- A generalization of Mallats classical multiresolution analysis, based on thetheory of spectral pairs, was considered in two articles by Gabardo and Nashed. In thissetting, the associated translation set is no longer a discrete subgroup of R but a spectrumassociated with a certain one-dimensional spectral pair and the associated dilation is aneven positive integer related to the given spectral pair. In this paper, we construct dualwavelets which are associated with Nonuniform Multiresolution Analysis. We show thatif the translates of the scaling functions of two multiresolution analyses are biorthogonal,then the associated wavelet families are also biorthogonal. Under mild assumptions onthe scaling functions and the wavelets, we also show that the wavelets generate Rieszbases
- Subjects :
- Pure mathematics
Discrete group
Generalization
Applied Mathematics
General Mathematics
Multiresolution analysis
010102 general mathematics
02 engineering and technology
01 natural sciences
Dilation (operator theory)
Wavelet
Integer
Biorthogonal system
0202 electrical engineering, electronic engineering, information engineering
020201 artificial intelligence & image processing
0101 mathematics
Scaling
Mathematics
Subjects
Details
- ISSN :
- 20739826 and 00492930
- Volume :
- 50
- Database :
- OpenAIRE
- Journal :
- Tamkang Journal of Mathematics
- Accession number :
- edsair.doi...........796c42aea155a89c597e3faea979507a