Wavelet packets: Uniform approximation and numerical integration

In this paper, it is proved that under some conditions, wavelet packet basis of [Formula: see text] can be used as a tool for the uniform approximation of an [Formula: see text]-times ([Formula: see text]) continuously differentiable and square integrable function [Formula: see text]. Sufficient conditions which establish that the approximations of wavelet packet sequences of square integrable function [Formula: see text] at lower levels are uniformly reliable and they uniformly approach zero as [Formula: see text] are given. Finally, a method based on wavelet packet expansion to find the definite integral of a function in [Formula: see text] is given and its error analysis has been discussed.