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.

The Structure and Properties of a Class of Affine Subspaces and Applications in Mechatronics Science

2013 ◽  
Vol 321-324 ◽  
pp. 2385-2388
Author(s):  
Su Luo Song
Keyword(s):  
Information Science ◽  
Fundamental Question ◽  
Orthogonal Complement ◽  
Affine Subspace ◽  
Wavelet Frame ◽  
Structure And Properties ◽  
Direct Sum ◽  
Affine Subspaces ◽  
Reducing Subspaces

Information science focuses on understanding problems from the perspective of the stakeholders involved and then applying information and other technologies as needed. 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. Motivated by the fundamental question as to whethor every affine subspace is singly-generated wavelet frame, we prove that every affine sub -space can be decomposed into the direct sum of a singly-generated afffine subspace.

The Traits of Canonical Banach Frames Generated by Multiple Scaling Functions and Applications in Applied Materials

2013 ◽  
Vol 684 ◽  
pp. 663-666
Author(s):  
Jing Li Gao ◽  
Shi Hui Cheng
Keyword(s):  
Scaling Functions ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Banach Frames ◽  
Parseval Frame ◽  
Single Function ◽  
Dilation Factor ◽  
Popular Subject ◽  
Frame Wavelets ◽  
Dual Wavelet

Frame theory has become a popular subject in scientific research during the past twenty years. In our study we use generalized multiresolution analyses in with dilation factor 4. We describe, in terms of the underlying multiresolution structure, all generalized multiresolution analyses Parseval frame wavelets all semi-orthogonal Parseval frame wavelets in . We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions. That is to say, the canonical dual wavelet frame cannot be generated by the translations and dilations of a single function. Traits of tight wavelet frames are presented.

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

scholarly journals Reducing Subspaces of Some Multiplication Operators on the Bergman Space over Polydisk

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Yanyue Shi ◽  
Na Zhou
Keyword(s):  
Bergman Space ◽  
Multiplication Operators ◽  
Direct Sum ◽  
Reducing Subspace ◽  
Reducing Subspaces

We consider the reducing subspaces ofMzNonAα2(Dk), wherek≥3,zN=z1N1⋯zkNk, andNi≠Njfori≠j. We prove that each reducing subspace ofMzNis a direct sum of some minimal reducing subspaces. We also characterize the minimal reducing subspaces in the cases thatα=0andα∈(-1,+∞)∖Q, respectively. Finally, we give a complete description of minimal reducing subspaces ofMzNonAα2(D3)withα>-1.

Thompson’s Group

2017 ◽  
Author(s):  
Sean Cleary
Keyword(s):  
Group Action ◽  
Word Length ◽  
Research Projects ◽  
Direct Sum ◽  
Group Presentations ◽  
Thompson’S Group ◽  
Rank 2 ◽  
Definition Of ◽  
Finitely Presented ◽  
Length Distortion

This chapter considers the Thompson's group F. Thompson's group F exhibits several behaviors that appear paradoxical. For example: F is finitely presented and contains a copy of F x F, indicating that F contains the direct sum of infinitely many copies of F. In addition, F has exponential growth but contains no free groups of rank 2. After providing an overview of the analytic definition and basic properties of the Thompson's group, the chapter introduces a combinatorial definition of F and two group presentations for F, an infinite one and a finite one. It also explores the subgroups, quotients, endomorphisms, and group action of F before concluding with an analysis of several geometric properties of F such as word length, distortion, dead ends, and growth. The discussion includes exercises and research projects.

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

SHIFT INVARIANT SPACES FOR LOCAL FIELDS

2011 ◽  
Vol 09 (03) ◽  
pp. 417-426 ◽  
Author(s):  
A. AHMADI ◽  
A. ASKARI HEMMAT ◽  
R. RAISI TOUSI
Keyword(s):  
Sufficient Conditions ◽  
Invariant Subspaces ◽  
Open Subgroup ◽  
Local Fields ◽  
Locally Compact Abelian Group ◽  
Compact Open Subgroup ◽  
Parseval Frame ◽  
Shift Invariant Spaces ◽  
Necessary And Sufficient ◽  
Invariant Spaces

This paper is an investigation of shift invariant subspaces of L2(G), where G is a locally compact abelian group, or in general a local field, with a compact open subgroup. In this paper we state necessary and sufficient conditions for shifts of an element of L2(G) to be an orthonormal system or a Parseval frame. Also we show that each shift invariant subspace of L2(G) is a direct sum of principle shift invariant subspaces of L2(G) generated by Parseval frame generators.

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