Size properties of wavelet packets generated using finite filters (Q1809934)

Summary: 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 basic 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 \(L^p[0,1)\).