ON CONVERGENCE OF WAVELET PACKET EXPANSIONS

It is well known that the Walsh-Fourier expansion of a function from the-block space (?)(0,1)), 1< q≤∞, converges pointwise a. e. We prove that the same result is true for the expansion of a function from (?) 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 Lp-functions, 1< p<∞. converges in norm and pointwise almost everywhere.