scholarly journals Equations for frame wavelets in $L^{2}(\mathbb{R}^{2})$

2016 ◽  
Vol 10 (3) ◽  
pp. 638-670
Author(s):  
Xingde Dai
Keyword(s):  
Frame Wavelets

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
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