一类小波级数函数图象的盒子维数

Box Dimension of Wavelet Series

讨论了小波级数的上、下盒子维数。在小波函数满足一定条件下，①证明了小波级数函数图象盒子维数的存在性；②给出了小波级数上、下盒子维数的最佳下界和最佳上界估计，并且证明了二者相等，由此可以利用小波系数计算它的盒子维数。③对小波级数也给出了它的Ｈａｕｓｄｏｒｆｆ维数的下界估计，进一步猜测其Ｈａｕｓｄｏｒｆｆ维数也存在并且等于它的盒子维数。

The super-box dimension and sub-box dimension of the wavelet series are discussed. When the wavelet function satisfies some conditions, the best super-bound and the best sub-bound are obtained. The existence of the box dimension of the wavelet series is proved and its box dimension by the wavelet coefficient may be calculated. The sub-boundary estimator of the Hausdorff dimension for the wavelet series is obtained, also. It is suggested that the Hausdorff dimension is existent and equals to the box dimension.