加权Sobolev空间中小波级数的收敛性

On Convergence of Wavelet Expansion in Weighted Sobolev Space

研究加权Sobolev空间中小波级数的收敛性与收敛速度.利用傅里叶级数的Parseval等式证明加权Sobolev空间中的小波级数是依范数收敛的,并在此基础上估计小波级数的余项,得到小波级数依范数收敛的速度的精确估计.

Convergence and convergence rate of wavelet expansion in weighted Sobolev space have been researched.By means of Parseval equality of Fourier series,it＇s proved that wavelet expansion in weighted Sobolev space converges in norm.Based on this,the remainder of wavelet expansion is estimated and exact estimation of convergence rate of wavelet expansion in norm obtained.