scholarly journals Semi-orthogonal frame wavelets and Parseval frame wavelets associated with GMRA

2008 ◽  
Vol 38 (5) ◽  
pp. 1449-1456 ◽  
Author(s):  
Zhanwei Liu ◽  
Guoen Hu ◽  
Guochang Wu ◽  
Bin Jiang
Keyword(s):  
Parseval Frame ◽  
Frame Wavelets ◽  
Orthogonal Frame

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.

scholarly journals MRA Parseval Frame Wavelets and Their Multipliers inL2(Rn)

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Wu Guochang ◽  
Yang Xiaohui ◽  
Liu Zhanwei
Keyword(s):  
Multiresolution Analysis ◽  
Scaling Functions ◽  
Parseval Frame ◽  
Integer Coefficients ◽  
Frame Wavelets

We characterize all generalized lowpass filters and multiresolution analysis(MRA) Parseval frame wavelets inL2(Rn)with matrix dilations of the form(Df)(x)=2f(Ax), where A is an arbitrary expandingn×nmatrix with integer coefficients, such that|det⁡A|=2. At first, we study the pseudo-scaling functions, generalized lowpass filters, and multiresolution analysis (MRA) Parseval frame wavelets and give some important characterizations about them. Then, we describe the multiplier classes associated with Parseval frame wavelets inL2(Rn)and give an example to prove our theory.

scholarly journals Further results on the connectivity of Parseval frame wavelets

2006 ◽  
Vol 134 (11) ◽  
pp. 3211-3221 ◽  
Author(s):  
G. Garrigós ◽  
E. Hernández ◽  
H. Šikić ◽  
F. Soria
Keyword(s):  
Parseval Frame ◽  
Frame Wavelets

SMOOTH PARSEVAL FRAMES FOR L2(ℝ) AND GENERALIZATIONS TO L2(ℝd)

2013 ◽  
Vol 11 (06) ◽  
pp. 1350047
Author(s):  
EMILY J. KING
Keyword(s):  
Higher Dimensions ◽  
Wavelet Sets ◽  
Parseval Frame ◽  
Wavelet Set ◽  
Parseval Frames ◽  
Schwartz Class ◽  
Frame Wavelets ◽  
Class Of Functions ◽  
Parseval Frame Wavelet ◽  
Provided Examples

Wavelet set wavelets were the first examples of wavelets that may not have associated multiresolution analyses. Furthermore, they provided examples of complete orthonormal wavelet systems in L2(ℝd) which only require a single generating wavelet. Although work had been done to smooth these wavelets, which are by definition discontinuous on the frequency domain, nothing had been explicitly done over ℝd, d > 1. This paper, along with another one cowritten by the author, finally addresses this issue. Smoothing does not work as expected in higher dimensions. For example, Bin Han's proof of existence of Schwartz class functions which are Parseval frame wavelets and approximate Parseval frame wavelet set wavelets does not easily generalize to higher dimensions. However, a construction of wavelet sets in [Formula: see text] which may be smoothed is presented. Finally, it is shown that a commonly used class of functions cannot be the result of convolutional smoothing of a wavelet set wavelet.

Parseval frame scaling sets and MSF Parseval frame wavelets

2009 ◽  
Vol 41 (4) ◽  
pp. 1966-1974 ◽  
Author(s):  
Zhanwei Liu ◽  
Guoen Hu ◽  
Zhibo Lu
Keyword(s):  
Parseval Frame ◽  
Frame Wavelets
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