小波级数的部分和的一致收敛性

摘要

The uniform convergence of the partial sum of wavelet expansions was discussed By introducing a functional space Lr2(R), the problem of uniform approximation of partial sum fm(r) of wavelet expansions of its r-th derivative f(r) to f(r) was studied. If f(r) were continuous on (a,b), an exact estimation of approximation rate of fm(r) to f(r) would be established, so that the result of related uniform convergence would be obtained.%讨论小波级数的部分和的一致收敛性.通过引入函数空间L2r(R),研究f∈L2r(R)的r阶导数f(r)m的小波级数的部分和f(r)m对f(r)的一致逼近问题.当f(r)在(a,b)上连续时,建立f(r)m逼近于f(r)的速度的一个精确估计,进而得到相关的一致收敛的结论.