二进仿射小波包

Dyadic affine wavelet packet

自从小波包概念提出以来 ,关于这一方面的研究吸引了许多数学家的兴趣。到目前为止 ,在L2 (RS)中关于正交与非正交小波包、可分与非可分小波包的研究已取得丰硕的成果 ,其中 S是一给定的自然数。CHUI和 LI在 R上有界一致连续函数空间上引入了插值多分辨分析的概念并给出了这一空间函数的二进仿射小波分解。本文在这一空间引入并利用泛函小波变换研究了二进仿射小波包 ,对这一空间的任一函数 ,给出了逐点收敛的二进仿射小波包分解 .

The study of wavelet packets has attracted interest of many mathematicians since its introduction. Up to now, rich results have been obtained about orthogonal and nonorthogonal wavelet packets, separable and nonseparable wavelet packets in \%L\%\+2(R\+S), where \%S\% is a fixed positive integer. CHUI and LI introduced the interpolating multiresolution analysis in the space of bounded and uniformly continuous functions defined on R and gave the dyadic affine wavelet decomposition of the functions in this space. The dyadic affine wavelet packet in this space is introduced and addressed in terms of functional wavelet transform. For any function in this space, a dyadic affine wavelet packet decomposition with pointwise convergence is obtained.