Two properties are given in this paper about the scaling Vj;j∈Z is a multiresolution analysis with a continuous scaling function φ which have compact support set and that φ the Fourier transform of φ is a continuo...Two properties are given in this paper about the scaling Vj;j∈Z is a multiresolution analysis with a continuous scaling function φ which have compact support set and that φ the Fourier transform of φ is a continuous real function,compactly supported, then φ(0)≠0 and when supp φ=[a1,b1]∪[a2,b2](b1< a2,0<a2), then we have a1≤0,0<b1,a1<b2/2≤b1,2π<b2-a1≤8π.展开更多
In this paper, we study the properties of periodic multiresolution analysis, and present a complete characterization of the scaling function sequence, which enables us to construct a new scaling function sequence from...In this paper, we study the properties of periodic multiresolution analysis, and present a complete characterization of the scaling function sequence, which enables us to construct a new scaling function sequence from a given one. An application of the main results is given at the end.展开更多
The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavel...The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavelet packets in higher dimensions is studied by means of Fourier transform and integral transform biorthogonality formulas concerning these wavelet packets are obtained.展开更多
文摘Two properties are given in this paper about the scaling Vj;j∈Z is a multiresolution analysis with a continuous scaling function φ which have compact support set and that φ the Fourier transform of φ is a continuous real function,compactly supported, then φ(0)≠0 and when supp φ=[a1,b1]∪[a2,b2](b1< a2,0<a2), then we have a1≤0,0<b1,a1<b2/2≤b1,2π<b2-a1≤8π.
文摘In this paper, we study the properties of periodic multiresolution analysis, and present a complete characterization of the scaling function sequence, which enables us to construct a new scaling function sequence from a given one. An application of the main results is given at the end.
基金Supported by Natural Science Foundation of Henan Province（0511013500）
文摘The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavelet packets in higher dimensions is studied by means of Fourier transform and integral transform biorthogonality formulas concerning these wavelet packets are obtained.
