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

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.

A New Procedure for Designing a Kind of Orthogonal Vector-Valued Multiscaled Wavelets and Wavelet Wraps

2011 ◽  
Vol 204-210 ◽  
pp. 1733-1736
Author(s):  
Hong Wei Gao
Keyword(s):  
Multiresolution Analysis ◽  
Filter Bank ◽  
Matrix Theory ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Orthogonal Vector ◽  
Novel Method ◽  
Necessary And Sufficient ◽  
Vector Valued

In this paper, notion of vector-valued multiresolution analysis is introduced. So does the notion of orthogonal vector-valued wavelets A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is presented by using paraunitary vector filter bank theory and matrix theory. A novel method for constructing a kind of orthogonal shortly supported vector -valued wavelets is presented.

Construction and Characteristics of Orthogonal Trivariate Multiwavelets with Finite Support

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.

An Optimization Algorithm for Orthogonal Trivariate Wavelets with Short Support

2012 ◽  
Vol 461 ◽  
pp. 835-839
Author(s):  
Ke Zhong Han
Keyword(s):  
Filter Bank ◽  
Scaling Function ◽  
Wavelet Packets ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Orthogonal Vector ◽  
Multi Scale ◽  
Dilation Factor ◽  
Necessary And Sufficient ◽  
Vector Valued

Wavelet analysis is nowadays a widely used tool in applied mathe-matics. The advantages of wavelet packets and their promising features in various application have attracted a lot of interest and effort in recent years.. The notion of vector-valued binary wavelets with two-scale dilation factor associated with an orthogonal vector-valued scaling function is introduced. The existence of orthogonal vector-valued wavelets with multi-scale is discussed. A necessary and sufficient condition is presented by means of vector-valued multiresolution analysis and paraunitary vector filter bank theory. An algorithm for constructing a sort of orthogonal vector-valued wave-lets with compact support is proposed, and their properties are investigated.

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 Nice Feature of Orthogonal Vector-Valued Bivariate Wavelet Packets with Arbitrary Integer Dilation Factor

2010 ◽  
Vol 439-440 ◽  
pp. 1184-1189
Author(s):  
Jian Tang Zhao ◽  
Jie Li
Keyword(s):  
Matrix Theory ◽  
Wavelet Packet ◽  
Wavelet Packets ◽  
Analysis Method ◽  
Arbitrary Integer ◽  
Time Frequency ◽  
Orthogonal Vector ◽  
Finite Group Theory ◽  
Dilation Factor ◽  
Vector Valued

In this paper, the notion of orthogonal vector-valued bivariate wavelet packets, which is a generalization of uni-wavelet packets, is introduced. A procedure for constructing them is presented. Their characteristics is investigated by using time-frequency analysis method, matrix theory and finite group theory. Orthogonality formulas are established. Orthonormal wavelet packet bases are obtained.

The Presentation of the Quarternary Super-Wavelet Wraps and Applications in Material Science

2013 ◽  
Vol 684 ◽  
pp. 469-472
Author(s):  
Jian Guo Shen
Keyword(s):  
Material Science ◽  
Materials Science ◽  
Dimensional Space ◽  
Tight Frame ◽  
Analysis Method ◽  
Necessary And Sufficient Condition ◽  
Time Frequency ◽  
Decomposition Scheme ◽  
Necessary And Sufficient ◽  
Vector Valued

Our goal is to obtain a character -ization of normalized tight frame super-wavelets The basis of materials science involves relating the desired properties and relative performance of a material in a certain application to the structure of the atoms and phases in that material through characterization. An approach for designing a sort of biorthogonal vector-valued wavelet wraps in four-dimensional space is presented and their biorthogonality traits are characterized by virtue of iteration method and time-frequency analysis method. The biorthogonality formulas concerning these wavelet wraps are established. A necessary and sufficient condition for the existence of the pyramid decomposition scheme of space is presented.

scholarly journals Semi-smooth Points in Some Classical Function Spaces

2021 ◽  
Vol 77 (1) ◽  
Author(s):  
Beata Derȩgowska ◽  
Beata Gryszka ◽  
Karol Gryszka ◽  
Paweł Wójcik
Keyword(s):  
Continuous Function ◽  
Metric Space ◽  
Continuous Functions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Compact Metric Space ◽  
Spaces Of Continuous Functions ◽  
Classical Function ◽  
Necessary And Sufficient ◽  
Vector Valued

AbstractThe investigations of the smooth points in the spaces of continuous function were started by Banach in 1932 considering function space $$\mathcal {C}(\Omega )$$ C ( Ω ) . Singer and Sundaresan extended the result of Banach to the space of vector valued continuous functions $$\mathcal {C}(\mathcal {T},E)$$ C ( T , E ) , where $$\mathcal {T}$$ T is a compact metric space. The aim of this paper is to present a description of semi-smooth points in spaces of continuous functions $$\mathcal {C}_0(\mathcal {T},E)$$ C 0 ( T , E ) (instead of smooth points). Moreover, we also find necessary and sufficient condition for semi-smoothness in the general case.

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.

Vector-valued nonuniform multiresolution analysis on local fields

2015 ◽  
Vol 13 (04) ◽  
pp. 1550029 ◽  
Author(s):  
Firdous Ahmad Shah ◽  
M. Younus Bhat
Keyword(s):  
Multiresolution Analysis ◽  
Orthonormal Basis ◽  
Positive Characteristic ◽  
Local Fields ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Vilenkin Groups ◽  
Refinement Mask ◽  
Necessary And Sufficient ◽  
Vector Valued

A multiresolution analysis (MRA) on local fields of positive characteristic was defined by Shah and Abdullah for which the translation set is a discrete set which is not a group. In this paper, we continue the study based on this nonstandard setting and introduce vector-valued nonuniform multiresolution analysis (VNUMRA) where the associated subspace V0 of L2(K, ℂM) has an orthonormal basis of the form {Φ (x - λ)}λ∈Λ where Λ = {0, r/N} + 𝒵, N ≥ 1 is an integer and r is an odd integer such that r and N are relatively prime and 𝒵 = {u(n) : n ∈ ℕ0}. We establish a necessary and sufficient condition for the existence of associated wavelets and derive an algorithm for the construction of VNUMRA on local fields starting from a vector refinement mask G(ξ) with appropriate conditions. Further, these results also hold for Cantor and Vilenkin groups.

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.

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