On convergence of wavelet packet expansions
Morten Nielsen · Analysis in Theory and Applications · 2002
It is well known that the-Walsh-Fourier expansion of a function from the block space B q ([0,1]), 1<q≤∞, converges pointwise a. e. We prove that the same result is true for the expansion of a function from B q in certain periodized smooth periodic non-stationary wavelet packets bases based on the Haar filters. We also consider wavelet packets based on the Shannon filters and show that the expansion of L p -functions, 1<p<∞, converges in norm and pointwise almost everywhere.