Wavelet packet approximation theorem for Hr type norm. Issue 3 (4th March 2019) - Khanna, Nikhil; Kaushik, S. K.
ABSTRACT: In this paper, we give the wavelet packet approximation theorem forH r type norm which can measure difference of the (weak) derivatives. We will show that with equal distribution of the vanishing moments between the scaling functionω 0 and the wavelet packetsω n, n ∈ N, if the sample values of a smooth function as scaling function coefficients at a fine scale are used, then the wavelet packet series approximates the smooth function under consideration with increasing verity inH r type norm as the number of vanishing moments M increases or the scale J gets finer.