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中文摘要：
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}meZ是一个拟正6序列，建立当m→＋∞时高维小波展开式的一致收敛定理。
英文摘要：
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 quasipositive 8 sequence, a uniformly convergent sequence is constructed and its pointwise convergence is obtained. Finally, it is proved that the reproducing kernel sequence {qm}meZ of a multiresolution analysis on certain conditions is a quasipositive 8 sequence, and a uniform convergence theorem on high-dimensional wavelet expansion is given when m→＋∞.
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