Size Properties of Wavelet Packets Generated Using Finite Filters
نویسنده
چکیده
We show that asymptotic estimates for the growth in L(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 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(R) for p 2. Finally, we show that the same type of results are true for the associated periodic wavelet packets in L[0, 1).
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