scholarly journals Multivariate FMRAs and FMRA frame wavelets for reducing subspaces of $L^{2}(\mathbb{R}^{d})$

2010 ◽  
Vol 50 (1) ◽  
pp. 83-99 ◽  
Author(s):  
Feng-Ying Zhou ◽  
Yun-Zhang Li
Keyword(s):  
Reducing Subspaces ◽  
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.

Reducing subspaces for the product of a forward and a backward operator-weighted shifts

2021 ◽  
Vol 501 (2) ◽  
pp. 125206
Author(s):  
Xu Tang ◽  
Caixing Gu ◽  
Yufeng Lu ◽  
Yanyue Shi
Keyword(s):  
Weighted Shifts ◽  
Reducing Subspaces

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

Joint dilation scaling sets on the reducing subspaces

2012 ◽  
Vol 3 (3) ◽  
Author(s):  
Niraj K. Shukla ◽  
Rajeshwari Dubey
Keyword(s):  
Reducing Subspaces

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.

scholarly journals TIME-SHIFTS GENERALIZED MULTIRESOLUTION ANALYSIS OVER DYADIC-SCALING REDUCING SUBSPACES

2004 ◽  
Vol 02 (03) ◽  
pp. 237-248 ◽  
Author(s):  
NHAN LEVAN ◽  
CARLOS S. KUBRUSLY
Keyword(s):  
Function Space ◽  
Multiresolution Analysis ◽  
Time Shift ◽  
Orthonormal Wavelet ◽  
Reducing Subspaces ◽  
Wandering Subspace ◽  
Generalized Multiresolution Analysis

A Generalized Multiresolution Analysis (GMRA) associated with a wavelet is a sequence of nested subspaces of the function space ℒ2(ℝ), with specific properties, and arranged in such a way that each of the subspaces corresponds to a scale 2m over all time-shifts n. These subspaces can be expressed in terms of a generating-wandering subspace — of the dyadic-scaling operator — spanned by orthonormal wavelet-functions — generated from the wavelet. In this paper we show that a GMRA can also be expressed in terms of subspaces for each time-shift n over all scales 2m. This is achieved by means of "elementary" reducing subspaces of the dyadic-scaling operator. Consequently, Time-Shifts GMRA associated with wavelets, as well as "sub-GMRA" associated with "sub-wavelets" will then be introduced.

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