Quasi-positive delta sequences and their applications in wavelet approximation (Q1751494)

Summary: A sufficient literature is available for the wavelet error of approximation of certain functions in the \(L^2\)-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, the wavelet estimator for the approximation of a function \(f\) belonging to \(\operatorname{Lip}_\alpha [a, b]\) class under supremum norm has been obtained. Working in this direction, four new theorems on the wavelet approximation of a function \(f\) belonging to \(\operatorname{Lip}_{\alpha}\), \(0 < \alpha \leq 1\) class using the projection \(P_m f\) of its wavelet expansions have been estimated. The calculated estimator is best possible in wavelet analysis.