Legendre Wavelet expansion of functions and their Approximations

Abstract

In this paper , nine new Legendre wavelet estimators of functions having bounded third and fourth derivatives have been obtained.These estimators are new and best approximation in wavelet analysis. Legendre wavelet estimator of a function f of bounded higher order derivatives is better and sharper than the estimator of a function f of bounded less order derivative.

Keywords

• legendre wavelet, legendre wavelet expansion, orthonormal basis,legendre wavelet approximation .