讨论周期函数的小波级数的收敛速度.通过对由小波函数构造的和式∑v∈Z(m,n)ψ(2mx+v)ψ(2mt+v)与f∈L1(T)的小波级数的部分和sN(f)的研究,从而对部分和sN(f)的收敛性及其收敛速度进行刻画,建立其中p-范数意义下收敛于f∈L1(T)的速度的精确估计,并指出周期函数的小波级数的部分和sN(f)在p-范数意义下以指数级的速度收敛于f.
Convergence rate of wavelet expansions of periodic functions is discussed. By studying the partial sum sN(f) of wavelet expansion of f∈L1(T) and the construction ∑v∈Z(m,n)ψ(2mx+v)ψ(2mt+v) , the convergence and convergence rate of partial sum of f∈L1(T) are characterized. And then an exact estimation of convergence rate of sN(f) to f≤L1(T) in the sense of p-norm is established.