The Orthogonality Characters of Multiple Vector-Valued Ternary Wavelets and Applications in Theoretical Physics

2011 ◽  
Vol 58-60 ◽  
pp. 1454-1459
Author(s):  
Hai Lin Gao
Keyword(s):  
Matrix Theory ◽  
Theoretical Physics ◽  
Operator Technique ◽  
Analysis Method ◽  
Orthonormal Wavelet ◽  
Time Frequency ◽  
Decomposition Scheme ◽  
Dilation Matrix ◽  
Active Research ◽  
Vector Valued

Wavelet analysis has been the focus of active research for twenty years, both in theory and applications. In this work, we develop the concept of a class of multiple vector-valued trivariate wavelet wraps with a dilation matrix. A new method for constructing multiple vector-valued trivariate wavelet wraps is proposed. Their characters are investigated by means of operator technique, time-frequency analysis method and matrix theory. There orthogonality formulas regarding the wavelet wraps are provided. Orthogonality decomposition relation formulas of the space L2(R3, Cr×r)are obtained by constructing a series of subspaces of the multiple vector-valued wavelet wraps. Furthermore, several orthonormal wavelet wrap bases of space L2(R3, Cr×r) are constructed from the wavelet wraps. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. Relation to theoretical physics is also discussed.

The Optimality Characters of Vector-Valued Binary Small-Wave Wraps with a Constant Dilation Factor

2011 ◽  
Vol 58-60 ◽  
pp. 1460-1465
Author(s):  
Ming Pu Guo
Keyword(s):  
Matrix Theory ◽  
Wavelet Packet ◽  
Analysis Method ◽  
Time Frequency ◽  
Decomposition Scheme ◽  
Finite Group Theory ◽  
Small Wave ◽  
Dilation Factor ◽  
Active Research ◽  
Vector Valued

Frame theory has been the focus of active research for twenty years, both in theory and applications. In this work, the notion of orthogonal vector-valued binary small-wave wraps, which is a generalization of uni-wavelet packets, is introduced. A procedure for constructing them is presented. Their orthogonality traits are investigated by using time-frequency analysis method, matrix theory and finite group theory. Orthogonality formulas concerning these binary small-wave wraps are established. Orthonormal wavelet packet bases are obtained. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided.

Specific Properties of a King of Trivariable Wavelet Packets with Respect to an Integer-Valued Dilation Matrix

2010 ◽  
Vol 439-440 ◽  
pp. 1141-1146
Author(s):  
Jin Cang Han ◽  
Yang Li
Keyword(s):  
Finite Group ◽  
Group Theory ◽  
Frequency Analysis ◽  
Matrix Theory ◽  
Wavelet Packets ◽  
Analysis Method ◽  
Time Frequency ◽  
Finite Group Theory ◽  
Dilation Matrix ◽  
Vector Valued

In the work, the concept of orthogonal vector-valued trivariate wavelet packets, which is a generalization of uniwavelet packets, is introduced. A new method for constructing them is developed, and their characteristics is discussed by using time-frequency analysis method, matrix theory and finite group theory. Orthogonality formulas are established.

The Properties of Multidimensional Semi-Orthogonal Frame Wavelet Packets

2010 ◽  
Vol 439-440 ◽  
pp. 896-901
Author(s):  
Qing Jiang Chen ◽  
Yu Ying Wang
Keyword(s):  
Matrix Theory ◽  
Wavelet Packet ◽  
Wavelet Packets ◽  
Analysis Method ◽  
Time Frequency ◽  
Dilation Matrix ◽  
Novel Method ◽  
Popular Subject ◽  
Vector Valued ◽  
Orthogonal Frame

Wavelet analysis has become a popular subject in scientific research during the past twenty years. In this work, we introduce the notion of vector-valued multiresolution analysis and vector-valued multivariate wavelet packets associated with an integer-valued dilation matrix. A novel method for constructing multi-dimen- -sional vector-valued wavelet packet is presented. Their characteristics are researched by means of operator theory, time-frequency analysis method and matrix theory. Three orthogonality formulas concerning the wavelet packets are established. Orthogonality decomposition relation formulas of the space are derived by constructing a series of subspaces of wavelet packets. Finally, one new orthonormal wavelet packet bases of are constructed from these wavelet packets.

The Traits of Two-Directional Orthogonal Multivariate Small-Wave Packages with Finite Support

2012 ◽  
Vol 430-432 ◽  
pp. 543-546
Author(s):  
Zhong Yin Chen
Keyword(s):  
Operator Theory ◽  
Matrix Theory ◽  
Wavelet Packet ◽  
Wavelet Packets ◽  
Analysis Method ◽  
Time Frequency ◽  
Dilation Matrix ◽  
Small Wave ◽  
Novel Method ◽  
Vector Valued

In this paper, we introduce the notion of vector-valued multiresolution analysis and two-directional vector-valued multivariate wavelet packages associated with an integer-valued dilation matrix. A novel method for constructing multi-dimensional vector-valued wavelet packet is presented. Their characteristics are researched by means of operator theory, time-frequency analysis method and matrix theory. Three orthogonality formulas concerning the wavelet packets are establ- lished. Orthogonality decomposition relation formulas of the space are derived by constru- cting a series of subspaces of wavelet packets.

The Characterization of a Kind of Vector-Valued Multivariate Wavelet Packets with Composite Dilation Matrix

2010 ◽  
Vol 439-440 ◽  
pp. 932-937
Author(s):  
Yin Hong Xia ◽  
Hua Li
Keyword(s):  
Operator Theory ◽  
Matrix Theory ◽  
Higher Dimensions ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Analysis Method ◽  
Time Frequency ◽  
Dilation Matrix ◽  
Vector Valued

In this article, the notion of a kind of multivariate vector-valued wavelet packets with composite dilation matrix is introduced. A new method for designing a kind of biorthogonal vector- valued wavelet packets in higher dimensions is developed and their biorthogonality property is inv- -estigated by virtue of matrix theory, time-frequency analysis method, and operator theory. Two biorthogonality formulas concerning these wavelet packets are presented. Moreover, it is shown how to gain new Riesz bases of space by constructing a series of subspace of wavelet packets.

The Properties of a Sort of Multidimensional Wavelet Packets According to an Integer-Valued Dilation Matrix

2010 ◽  
Vol 108-111 ◽  
pp. 1021-1026
Author(s):  
Bao Ming Qiao ◽  
Xue Jun Qiao
Keyword(s):  
Matrix Theory ◽  
Wavelet Packet ◽  
Wavelet Packets ◽  
Analysis Method ◽  
Time Frequency ◽  
The Past ◽  
Dilation Matrix ◽  
Popular Subject ◽  
The Space L2 ◽  
Vector Valued

Wavelet analysis has become a popular subject in scientific research in the past twenty years. In this work, we develop the concept of a class of vector-valued multivarition matrix. A new method for constructing multidimensional vector-valued wavelet packets is formulated. Their characteristics are researched by means of operator theory, time-frequency analysis method and matrix theory. There orthogonality formulas regarding the wavelet packets are provided. Orthogonality decomposition relation formulas of the space L2(Rs)r are obtained by constructing a series of subspaces of the vector-valued wavelet packet. Furthermore, several orthonormal wavelet packet bases of space L2(Rs)r are constructed from the wavelet packets.

The Research of a Two-Directional Vector-Valued Quarternary Wavelet Packets and Applications in Material Engineering

2013 ◽  
Vol 712-715 ◽  
pp. 2487-2492
Author(s):  
Jian Feng Zhou
Keyword(s):  
Functional Analysis ◽  
Frequency Analysis ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Sufficient Condition ◽  
Subdivision Scheme ◽  
Analysis Method ◽  
Time Frequency ◽  
Dilation Matrix ◽  
Vector Valued

In this paper, we introduce a class of vector-valued four-dimensional wavelet packets according to a dilation matrix, which are generalizations of univariate wavelet packets. The defini -tion of biorthogonal vector four-dimensional wavelet packets is provided and their biorthogonality quality is researched by means of time-frequency analysis method, vector subdivision scheme and functional analysis method. Three biorthogonality formulas regarding the wavelet packets are established. Finally, it is shown how to draw new Riesz bases of space from these wavelet packets. The sufficient condition for the existence of four-dimensional wavelet packets is established based on the multiresolution analysis method.

The Presentation of Biorthogonal Non-Tensor Trivariate Wavelet Wraps in Besov Space

2012 ◽  
Vol 461 ◽  
pp. 738-742
Author(s):  
De Lin Hua
Keyword(s):  
Besov Space ◽  
Frequency Analysis ◽  
Iteration Method ◽  
Filter Bank ◽  
Matrix Theory ◽  
Analysis Method ◽  
Analogy Method ◽  
Time Frequency ◽  
Orthonormal Bases ◽  
Vector Valued

In this paper, the concept of orthogonal non-tensor bivariate wavelet packs, which is the generalization of orthogonal univariate wavelet packs, is pro -posed by virtue of analogy method and iteration method. Their orthogonality property is investigated by using time-frequency analysis method and variable se-paration approach. Three orthogonality formulas regarding these wavelet wraps are established. Moreover, it is shown how to draw new orthonormal bases of space from these wavelet wraps. A procedure for designing a class of orthogonal vector-valued finitely supported wavelet functions is proposed by virtue of filter bank theory and matrix theory.

The Biorthogonality Property of the Multidimensional Wavelet Packets with Multi-Scale Factor

2010 ◽  
Vol 439-440 ◽  
pp. 1093-1098
Author(s):  
Jian Feng Zhou ◽  
Ping An Wang
Keyword(s):  
Frequency Analysis ◽  
Operator Theory ◽  
Matrix Theory ◽  
Higher Dimensions ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Analysis Method ◽  
Time Frequency ◽  
Multi Scale ◽  
Vector Valued

In this article, we introduce a sort of vector-valued wavelet packets with multi-scale dilation of space , which are generalizations of multivariaale wavelet packets. A method for designing a sort of biorthogonal vector-valued wavelet packets in higher dimensions is presented and their biorthogonality property is characterized by virtue of time-frequency analysis method, matrix theory, and operator theory. Three biorthogonality formulas regarding these wavelet packets are established. Furtherore, it is shown how to obtain new Riesz bases of space from these wavelet packets.

The Characteristics Concerning a Class of Orthogonal Multivariate Matrix-Valued Scaling Functions and Frame Packets

2013 ◽  
Vol 321-324 ◽  
pp. 1317-1320
Author(s):  
Hong Yun Liu ◽  
Jie Li
Keyword(s):  
Functional Analysis ◽  
Materials Science ◽  
Matrix Theory ◽  
Orthogonal Matrix ◽  
Wavelet Packets ◽  
Scaling Functions ◽  
Analysis Method ◽  
Orthonormal Wavelet ◽  
Time Frequency ◽  
Analysis Design

Mechanical engineering is a discipline of engineering that applies the principles of physics and materials science for analysis, design, manufacturing, and maintenance of mechanical systems. In this work, the notion of matrix-valued multiresolution analysis of space is introduced. A method for constructing orthogonal matrix-valued ternary wavelet packs is developed and their properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these wavelet packets are provided. Finally, new orthonormal wavelet pack bases of space are obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.

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