Pointwise convergence and uniform convergence for wavelet frame series is a new topic. With the help of band-limited dual wavelet frames, this topic is first researched.
Suppose M and N are two r×r and s×s dilation matrices,respectively.LetΓM andΓN represent the complete sets of representatives of distinct cosets of the quotient groups M-T Zr/Zr and N-T Zs/Zs,respectively....Suppose M and N are two r×r and s×s dilation matrices,respectively.LetΓM andΓN represent the complete sets of representatives of distinct cosets of the quotient groups M-T Zr/Zr and N-T Zs/Zs,respectively.Two methods for constructing nonseparable Ω-filter banks from M-filter banks and N-filter banks are presented,where Ω is a（r＋s） ×（r＋s） dilation matrix such that one of its complete sets of representatives of distinct cosets of the quotient groups Ω-T Zr＋s/Zr＋s areΓΩ={[γT h,ζ T q] T：γh∈ΓM,ζq∈ΓN}.Specially,Ω can be [MΘ0N],whereΘis a r×s integer matrix with M-1Θbeing also an integer matrix.Moreover,if the constructed filter bank satisfies Lawton＇s condition,which can be easy to verify,then it generates an orthonormal nonseparable Ω-wavelet basis for L2（Rr＋s）.Properties,including Lawton＇s condition,vanishing moments and regularity of the new Ω-filter banks or new Ω-wavelet basis are discussed then.Finally,a class of nonseparable Ω-wavelet basis for L2（Rr＋1） are constructed and three other examples are given to illustrate the results.In particular,when M=N=2,all results obtained in this paper appeared in[1].展开更多
文摘Pointwise convergence and uniform convergence for wavelet frame series is a new topic. With the help of band-limited dual wavelet frames, this topic is first researched.
基金Supported by the National Natural Science Foundation of China(11071152)the Natural Science Foundation of Guangdong Province(10151503101000025)
文摘Suppose M and N are two r×r and s×s dilation matrices,respectively.LetΓM andΓN represent the complete sets of representatives of distinct cosets of the quotient groups M-T Zr/Zr and N-T Zs/Zs,respectively.Two methods for constructing nonseparable Ω-filter banks from M-filter banks and N-filter banks are presented,where Ω is a（r＋s） ×（r＋s） dilation matrix such that one of its complete sets of representatives of distinct cosets of the quotient groups Ω-T Zr＋s/Zr＋s areΓΩ={[γT h,ζ T q] T：γh∈ΓM,ζq∈ΓN}.Specially,Ω can be [MΘ0N],whereΘis a r×s integer matrix with M-1Θbeing also an integer matrix.Moreover,if the constructed filter bank satisfies Lawton＇s condition,which can be easy to verify,then it generates an orthonormal nonseparable Ω-wavelet basis for L2（Rr＋s）.Properties,including Lawton＇s condition,vanishing moments and regularity of the new Ω-filter banks or new Ω-wavelet basis are discussed then.Finally,a class of nonseparable Ω-wavelet basis for L2（Rr＋1） are constructed and three other examples are given to illustrate the results.In particular,when M=N=2,all results obtained in this paper appeared in[1].
