Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation

A sufficient literature is available for the wavelet error of approximation of certain functions in theL2-norm. There is no work in context of multiresolution approximation of a function in the sense of sup-error. In this paper, for the first time, wavelet estimator for the approximation of a functionfbelonging toLipα[a,b]class under supremum norm has been obtained. Working in this direction, four new theorems on the wavelet approximation of a functionfbelonging toLipα,0<α≤1class using the projectionPmfof its wavelet expansions have been estimated. The calculated estimator is best possible in wavelet analysis.