Sobolev空间中小波级数的一致收敛性

Uniform Convergence of Wavelet Expansion in Sobolev Space

应用Parseval等式对Sobolev空间中的小波级数的余项变形之后,利用Cauchy不等式与放缩的方法对其进行讨论与估计,建立小波级数的余项一致收敛于0的速度的精确估计,从而得到小波级数的一致收敛性与一致收敛的速度的精确估计.

By using Parseval equality, the remainder of wavelet expansion is deformated in Sobolev space. By means of Cauchy inequality and amplification, the remainder of wavelet expansion is dicussed and studied. Then exact estimation of uniform convergence rate of the remainder to 0 is established. Finally, uniform convergence and exact estimation of uniform convergence rate of wavelet expansion are obtained.