Abstract:

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→+∞.

Key words:  high-dimensional wavelet expansion; uniform convergence; quasi-positive δ sequence