Open Access
June, 2002 Size properties of wavelet packets generated using finite filters
Morten Nielsen
Rev. Mat. Iberoamericana 18(2): 249-265 (June, 2002).


We show that asymptotic estimates for the growth in $L^p(\mathbb{r})$-norm of a certain subsequence of the basic wavelet packets associated with a finite filter can be obtained in terms of the spectral radius of a subdivision operator associated with the filter. We obtain lower bounds for this growth for $p\gg 2$ using finite dimensional methods. We apply the method to get estimates for the wavelet packets associated with the Daubechies, least asymmetric Daubechies, and Coiflet filters. A consequence of the estimates is that such basis wavelet packets cannot constitute a Schauder basis for $L^p(\mathbb{R})$ for $p\gg 2$. Finally, we show that the same type of results are true for the associated periodic wavelet packets in $L^p[0,1)$.


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Morten Nielsen. "Size properties of wavelet packets generated using finite filters." Rev. Mat. Iberoamericana 18 (2) 249 - 265, June, 2002.


Published: June, 2002
First available in Project Euclid: 28 April 2003

zbMATH: 1029.42034
MathSciNet: MR1949828

Primary: 42

Keywords: $L^p$-convergence , Schauder basis , subdivision operators , wavelet analysis , wavelet packets

Rights: Copyright © 2002 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.18 • No. 2 • June, 2002
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