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

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.

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

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.439-440.1093 ◽

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.

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Construction and Characteristics of Orthogonal Trivariate Multiwavelets with Finite Support

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.461.860 ◽

2012 ◽

Vol 461 ◽

pp. 860-863

Author(s):

De Lin Hua ◽

Ruo Hui Liu

Keyword(s):

Filter Bank ◽

Materials Science ◽

Matrix Theory ◽

New Method ◽

Analysis Method ◽

Time Frequency ◽

Orthogonal Vector ◽

Fundamental Properties ◽

Necessary And Sufficient ◽

Vector Valued

Materials science also deals with fundamental properties and characteristics of materi- als.In this paper, the notion of orthogonal vector-valued wavelets is introduced. A new method for constructing associated multiwavelets from multi-scaling functions is presented which is simple for computation. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is presented by using paraunitary vector filter bank theory, time-frequency analysis method and matrix theory. A new method for constructing a class of orthogonal finitectly supported vector-valued wavelets is presented.

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Generation and Characteristics of a Class of Four-Dimensional Multiwavelet Packets with Six-Scale Dilation Factor

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.460-461.317 ◽

2011 ◽

Vol 460-461 ◽

pp. 317-322

Author(s):

Qing Jiang Chen ◽

Zong Tian Wei

Keyword(s):

Frequency Analysis ◽

Operator Theory ◽

Matrix Theory ◽

Higher Dimensions ◽

Wavelet Packets ◽

Riesz Bases ◽

Analysis Method ◽

Time Frequency ◽

Dilation Factor ◽

Vector Valued

In this paper, we introduce a class of vector-valued wavelet packets of space , which are generalizations of multivariate wavelet packets. A procedure for constructing a class of biorthogonal vector-valued wavelet packets in higher dimensions is presented and their biorthogonality properties are characterized by virtue of matrix theory, time-frequency analysis method, and operator theory. Three biorthogonality formulas regarding these wavelet packets are derived. Moreover, it is shown how to gain new Riesz bases of space from these wavelet packets.

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Construction and Characteristics of a Kind of Four-Dimensional Vector Wavelet Packets with Four-Scale Dilation

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.20-23.1053 ◽

2010 ◽

Vol 20-23 ◽

pp. 1053-1059

Author(s):

Xin Xian Tian ◽

Ai Lian Huo

Keyword(s):

Frequency Analysis ◽

Operator Theory ◽

Matrix Theory ◽

Higher Dimensions ◽

Wavelet Packets ◽

Riesz Bases ◽

Dimensional Vector ◽

Analysis Method ◽

Time Frequency ◽

Vector Valued

In this paper, we introduce a class of vector-valued wavelet packets of space , which are generalizations of multivariate wavelet packets. A procedure for constructing a class of biorthogonal vector-valued wavelet packets in higher dimensions is presented and their biorthogonality properties are characterized by virtue of matrix theory, time-frequency analysis method, and operator theory. Three biorthogonality formulas regarding these wavelet packets are derived. Moreover, it is shown how to gain new Riesz bases of space from these wavelet packets.

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Characterization of the Quarternary Wavelet Wraps with Multi-Scale Factor and Applications in Physics

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.461.656 ◽

2012 ◽

Vol 461 ◽

pp. 656-660

Author(s):

Hai Lin Gao

Keyword(s):

Frequency Analysis ◽

Operator Theory ◽

Matrix Theory ◽

Wavelet Packets ◽

Riesz Bases ◽

Analysis Method ◽

Time Frequency ◽

Multi Scale ◽

Vector Valued

In t In this article, we introduce a sort of vector-valued wavelet wraps with multi-scale dilation of space L 2(Rn, Cv) , which are generaliza-tions of multivariaale wavelet wraps. A method for designing a sort of biorthogonal vector-valued wavelet wraps 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 L 2(Rn, Cv) from these wavelet wraps.

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A Novel Approach for Constructing a Class of Orthogon Vector-Valued Wavelets with Finite Support

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.439-440.1123 ◽

2010 ◽

Vol 439-440 ◽

pp. 1123-1128

Author(s):

Shui Wang Guo ◽

Jin Chang Shi

Keyword(s):

Filter Bank ◽

Matrix Theory ◽

Sufficient Condition ◽

Analysis Method ◽

Necessary And Sufficient Condition ◽

Time Frequency ◽

Orthogonal Vector ◽

Novel Approach ◽

Necessary And Sufficient ◽

Vector Valued

In this paper, the notion of orthogonal vector-valued wavelets is introduced. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is presented by using paraunitary vector filter bank theory, time-frequency analysis method and matrix theory. A new method for constructing a class of orthog- -onal finitectly supported vector-valued wavelets is presented.

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.712-715.2487 ◽

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.

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A Study of Matrix-Valued Trivariate Wavelet Packets Associated with an Orthogonal Matrix-Valued Trivariate Scaling Function

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.439-440.1165 ◽

2010 ◽

Vol 439-440 ◽

pp. 1165-1170

Author(s):

Jian Zhang ◽

Shui Wang Guo

Keyword(s):

Functional Analysis ◽

Frequency Analysis ◽

Multiresolution Analysis ◽

Matrix Theory ◽

Scaling Function ◽

Orthogonal Matrix ◽

Wavelet Packets ◽

Riesz Bases ◽

Analysis Method ◽

Time Frequency

Wavelet analysis has become a developing branch of mathematics for over twenty years. In this paper, the notion of matrix-valued multiresolution analysis of space is introduced. A method for constructing biorthogonal matrix–valued trivariate wavelet packets is developed and their properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three biorthogonality formulas concerning these wavelet packets are provided. Finally, new Riesz bases of space is obtained by constructing a series of subspaces of biorthogonal matrix-valued wavelet packets.

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.58-60.1460 ◽

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.

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