Uniform convergence of high-dimensional wavelet expansions
Zhao Shu-gai · Journal of Shandong University · 2010
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 {qm}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→+∞.