Acta mathematica scientia, Series B >
A CLASS OF MULTIWAVELETS AND PROJECTED FRAMES FROM TWO-DIRECTION WAVELETS
Received date: 2011-12-28
Revised date: 2013-03-14
Online published: 2014-03-20
Supported by
The first author is supported by the Natural Science Foundation China (11126343) and Guangxi Natural Science Foundation (2013GXNSFBA019010). The second author is supported by Natural Science Foundation China (11071152) and Natural Science Foundation of Guangdong Province (10151503101000025, S2011010004511).
This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R*, s > 1. We give a sufficient condition for a two-direction refinable function belonging to L2(R*). Then, two theorems are given for constructing biorthogonal (orthogonal) two-direction refinable functions in L2(R*) and their biorthogonal (orthogo-nal) two-direction wavelets, respectively. From the constructed biorthogonal (orthogonal) two-direction wavelets, symmetric biorthogonal (orthogonal) multiwaveles in L2(R*) can be obtained easily. Applying the projection method to biorthogonal (orthogonal) two-direction wavelets in L2(R*), 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.
LI You-Fa , YANG Shou-Zhi . A CLASS OF MULTIWAVELETS AND PROJECTED FRAMES FROM TWO-DIRECTION WAVELETS[J]. Acta mathematica scientia, Series B, 2014 , 34(2) : 285 -300 . DOI: 10.1016/S0252-9602(14)60005-9
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