SIZE PROPERTIES OF WAVELET PACKETS GENERATED USING FINITE FILTERS

Abstract. We show that asymptotic estimates for the growth in Lp(R)-norm of a certain sub-sequence 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 es-timates 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 Lp(R) for p 2. Finally, we show that the same type of results are true for the associated periodic wavelet packets in Lp[0, 1)