高维小波展开式的一致收敛性

研究高维小波展开式的部分和的一致收敛性。建立当m→-∞时高维小波展开式的一致收敛定理;其次,通过引入拟正δ序列的概念,构造一个一致逼近序列并得到该序列的逐点收敛性;最后,通过证明多分辨分析的再生核序列{qm}m∈Z是一个拟正δ序列,建立当m→+∞时高维小波展开式的一致收敛定理。

Uniform convergence of high-dimensional wavelet expansions

Uniform convergence of high-dimensional wavelet expansions is discussed. First, a uniform convergence theorem on high-dimensional wavelet expansion is established when m→-∞.Then, by introducing the concept of a quasi-positive δ sequence, a uniformly convergent sequence is constructed and its pointwise convergence is obtained. Finally, it is proved that the reproducing kernel sequence ｛q_m｝_m∈Z of a multiresolution analysis on certain conditions is a quasi-positive δ sequence, and a uniform convergence theorem on high-dimensional wavelet expansion is given when m→+∞.