scholarly journals Frame wavelets with matrix dilations in L2(Rn)

2004 ◽  
Vol 17 (6) ◽  
pp. 631-639 ◽  
Author(s):  
Deyun Yang ◽  
Xingwei Zhou
Keyword(s):  
Frame Wavelets

scholarly journals Characterizations of Tight Frame Wavelets with Special Dilation Matrices

2010 ◽  
Vol 2010 ◽  
pp. 1-26 ◽  
Author(s):  
Huang Yongdong ◽  
Zhu Fengjuan
Keyword(s):  
Linear Space ◽  
Multiresolution Analysis ◽  
Nonnegative Integer ◽  
Tight Frame ◽  
Dilation Matrix ◽  
Low Pass ◽  
Dimension Functions ◽  
Frame Wavelets ◽  
Low Pass Filters

We study all generalized low-pass filters and tight frame wavelets with special dilation matrixM(M-TFW), whereMsatisfiesMd=2Idand generates the checkerboard lattice. Firstly, we study the pseudoscaling function, generalized low-pass filters and multiresolution analysis tight frame wavelets with dilation matrixM(MRA M-TFW), and also give some important characterizations about them. Then, we characterize all M-TFW by showing precisely their corresponding dimension functions which are nonnegative integer valued. Finally, we also show that an M-TFW arises from our MRA construction if and only if the dimension of a particular linear space is either zero or one.

Connectivity in the set of Tight Frame Wavelets (TFW)

2003 ◽  
Vol 38 (1) ◽  
pp. 75-98 ◽  
Author(s):  
Gustavo Garrigos
Keyword(s):  
Tight Frame ◽  
Frame Wavelets

Semi-orthogonal wavelet frames on local fields

Analysis ◽  
2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Firdous A. Shah ◽  
M. Younus Bhat
Keyword(s):  
Finite Number ◽  
Positive Characteristic ◽  
Local Fields ◽  
Wavelet Frames ◽  
Orthogonal Wavelet ◽  
Basic Equations ◽  
Frame Multiresolution Analysis ◽  
Frame Wavelets ◽  
Equivalent Conditions

AbstractWe investigate semi-orthogonal wavelet frames on local fields of positive characteristic and provide a characterization of frame wavelets by means of some basic equations in the frequency domain. The theory of frame multiresolution analysis recently proposed by Shah [J. Operators (2015), Article ID 216060] on local fields is used to establish equivalent conditions for a finite number of functions

The Closure of the Set of Tight Frame Wavelets

2008 ◽  
Vol 107 (1-3) ◽  
pp. 195-201 ◽  
Author(s):  
Marcin Bownik
Keyword(s):  
Tight Frame ◽  
Frame Wavelets

Semi-Orthogonal Parseval Wavelets Frames on Local Fields and Applications in Manufacturing Science

2013 ◽  
Vol 712-715 ◽  
pp. 2464-2468
Author(s):  
Shi Heng Wang
Keyword(s):  
Local Fields ◽  
Affine Subspace ◽  
Parseval Frame ◽  
Direct Sum ◽  
Reducing Subspaces ◽  
Dilation Factor ◽  
Definition Of ◽  
Frame Wavelets ◽  
Manufacturing Science ◽  
Orthogonal Frame

Manufacturing science focuses on understanding problems from the perspective of the stakeholders involved and then applying manufacturing science as needed. We investigate semi-orthogonal frame wavelets and Parseval frame wavelets in with a dilation factor. We show that every affine subspace is the orthogonal direct sum of at most three purely non-reducing subspaces. This result is obtained through considering the basicquestion as to when the orthogonal complement of an afffine subspace in another one is still affine subspace.The definition of multiple pseudofames for subspaces with integer translation is proposed. The notion of a generalized multiresolution structure of is also introduced. The construction of a generalized multireso-lution structure of Paley-Wiener subspaces of is investigated.

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