数学物理学报（英文版）
數學物理學報（英文版）
수학물이학보（영문판）
ACTA MATHEMATICA SCIENTIA
2014年
2期
285-300
,共16页
Two-direction refinable functions%two-direction wavelets%multiwavelets%wavelet frames%biothogonal (orthogonal)%symmetry%projection method
This article aims at studying two-direction refinable functions and two-direction wavelets in the setting Rs, s>1. We give a sufficient condition for a two-direction refinable function belonging to L2(Rs). Then, two theorems are given for constructing biorthogonal (orthogonal) two-direction refinable functions in L2(Rs) and their biorthogonal (orthogo-nal) two-direction wavelets, respectively. From the constructed biorthogonal (orthogonal) two-direction wavelets, symmetric biorthogonal (orthogonal) multiwaveles in L2(Rs) can be obtained easily. Applying the projection method to biorthogonal (orthogonal) two-direction wavelets in L2(Rs), we can get dual (tight) two-direction wavelet frames in L2(Rm), where m≤s. From the projected dual (tight) two-direction wavelet frames in L2(Rm), symmetric dual (tight) frames in L2(Rm) can be obtained easily. In the end, an example is given to illustrate theoretical results.
