## Revista Matemática Iberoamericana

### Size properties of wavelet packets generated using finite filters

Morten Nielsen

#### Abstract

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 $L^p[0,1)$.

#### Article information

Source
Rev. Mat. Iberoamericana, Volume 18, Number 2 (2002), 249-265.

Dates
First available in Project Euclid: 28 April 2003

https://projecteuclid.org/euclid.rmi/1051544237

Mathematical Reviews number (MathSciNet)
MR1949828

Zentralblatt MATH identifier
1029.42034

Subjects
Primary: 42

#### Citation

Nielsen, Morten. Size properties of wavelet packets generated using finite filters. Rev. Mat. Iberoamericana 18 (2002), no. 2, 249--265. https://projecteuclid.org/euclid.rmi/1051544237

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