Some Research About The Wavelets Approximation

In this paper, we study the Shonnon wavelet approximations and its appli-cations, research the approximation degree. The paper consists of three chapters , The main contents are as follows.In Chapter 1, we introduce the theory of approximation of functions and wavelets and the main results in this paper. Sun X.H[4] established an estimate of the convergence rate if f∈G L2(R) is continuous in (a, b) and φ(x) satisfies the conditionIn Chapter 2, we discuss the convergence rate of Shonnon wavelet expansion for ABMV functions.We will prove that if f(x) ∈ L2(R) ∩ ABMV[x-δ,x+δ] ,thenIn Chapter 3, we give an estimation of convergence rate of conjugate Shonnon wavelets for jumps of functions at their discontinuities.