L^2(R^n)上的半正交多小波框架

Semi-orthogonal multiwavelet frames in L^2(R^n)

本文研究L2(Rn)上伸缩矩阵A满足|detA|>1的半正交多小波框架.本文得到半正交和严格半正交框架的一系列性质及刻画.本文证明半正交Parseval多小波框架与广义多分辨分析(GMRA)Parseval多小波框架是等价的.特别地,本文利用最小频率支撑(MSF)多小波框架和小波集,构造若干半正交多小波框架的例子.

We investigate semi-orthogonal multiwavelet frames with matrix dilation that ｜detA｜ 〉 1 in L^2（R^n） and obtain some characterizations of strictly semi-orthogonal multiwavelet frames. We find the equivalence of semi-orthogonal Parseval multiwavelet frames and Generalized Multiresolution Analysis （GMRA） multiwavelet Parseval frames. In particular, we discuss the semi-orthogonality of minimally support frequency （MSF） multiwavelet frames, and construct some examples of semi-orthogonal multiwavelet frames by wavelet sets.