Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation

Abstract

A sufficient literature is available for the wavelet error of approximation of certain functions in the L2-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 function f belonging to Lipα[a,b] class under supremum norm has been obtained. Working in this direction, four new theorems on the wavelet approximation of a function f belonging to Lipα, 0 < α ≤ 1 class using the projection Pmf of its wavelet expansions have been estimated. The calculated estimator is best possible in wavelet analysis. © 2016 Shyam Lal and Susheel Kumar.