The Description of the Semi-Local Hardy Space by Gabor Frames

2013 ◽  
Vol 321-324 ◽  
pp. 2380-2384
Author(s):  
Jin Shun Feng
Keyword(s):  
Hardy Space ◽  
Materials Science ◽  
Gabor Frames ◽  
Constructive Method ◽  
Sufficient Condition ◽  
Science And Engineering ◽  
Decomposition Scheme ◽  
Interdisciplinary Field ◽  
Local Hardy Space ◽  
Affine Frames

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this work, the notion of the binary generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of binary multiscale pseudo- -frames for subspaces is investigated. The construction of a GMS of Paley-Wiener subspace of L^2(R^2) is studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of L^2(R^2) based on a BGMS is established.

The Research of Dual Quarternary Pseudoframes for Hardy Space and Applications in Engineering Materials

2014 ◽  
Vol 977 ◽  
pp. 19-24
Author(s):  
Chun Yi Jiao ◽  
Shi Heng Wang
Keyword(s):  
Hardy Space ◽  
Materials Science ◽  
Constructive Method ◽  
Sufficient Condition ◽  
Science And Engineering ◽  
Decomposition Scheme ◽  
Interdisciplinary Field ◽  
Affine Frames ◽  
Engineering Materials

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering.. In this work, the notion of the quarternary generalized multiresol- ution structure (TGMS) of subspace is proposed. The characteristics of quarternary affine pseudoframes for subspaces is investigated. Construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a TGMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a TGMS is established.

Study of Trivariate Pseudoframes and Subspace Frames and their Applications in Solid-State Physics

2012 ◽  
Vol 459 ◽  
pp. 262-265
Author(s):  
Zhong Yin Chen ◽  
Qing Jiang Chen
Keyword(s):  
State Physics ◽  
Solid State ◽  
Materials Science ◽  
Constructive Method ◽  
Sufficient Condition ◽  
Solid State Physics ◽  
Science And Engineering ◽  
Ion Structure ◽  
Decomposition Scheme ◽  
Interdisciplinary Field

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering.. In this work, the notion of the trivariate generalized multiresolut- ion structure (TGMS) of subspace is proposed. The characteristics of trivariate affine pseudoframes for subspaces is investigated. Construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a TGMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a TGMS is established.

The Traits of Nontensor Five-Variant Wavelet Packs and Applications in Management Science and Materials Science

2012 ◽  
Vol 461 ◽  
pp. 868-871 ◽  
Author(s):  
Qing Ge Zhang
Keyword(s):  
Functional Analysis ◽  
Materials Science ◽  
Constructive Method ◽  
Sufficient Condition ◽  
Analysis Method ◽  
Orthogonal Wavelet ◽  
Science And Engineering ◽  
Interdisciplinary Field ◽  
Novel Approach ◽  
Generalized Multiresolution Analysis

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this article, the notion of orthogonal nonseparable five-variant wavelet packages is presented. A novel approach for constructing them is presented by iteration method and functional analysis method. A feasible approach for constructing two-directional orthogonal wavelet packs is developed. The orthogonality property of five-variant wavelet packs is discussed. Three orthogonality formulas concerning these wavelet packs are estabished. A constructive method for affine frames of is proposed. The sufficient condition for the existence of a class of affine pseudoframes with filter banks is obtained by virtue of a generalized multiresolution analysis.

Parameterization of Masks for Tight Wavelet Frames and Multiple Pseudoframes and Applications in Mechanical Engineering

2014 ◽  
Vol 915-916 ◽  
pp. 1448-1451
Author(s):  
Yu Min Yu
Keyword(s):  
Mechanical Engineering ◽  
Materials Science ◽  
Constructive Method ◽  
Sufficient Condition ◽  
Wavelet Frames ◽  
Decomposition Scheme ◽  
Symmetric Extension ◽  
Analysis Design ◽  
Affine Frames ◽  
Resolution Structure

Mechanical engineering is a discipline of engineering that applies the principles of engine ering, physics and materials science for analysis, design, manufacturing, and maintenance of mecha nical systems. In this work, the construction of 4-band tight wavelet frames with symmetric proper-ties using symmetric extension and parameterization of the paraunitary matrix. The notion of an 4-band generalized multiresolution structure of subspace is proposed. The characteristics of affine pseudoframes for subspaces is investigated. The construction of a generalized multiresolution structure of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obta-ined based on such a generalized multiresolution structure and a sufficient condition for its exist-ence is presented. A constructive method for affine frames of based on a generalized multi-resolution structure is presented.

Study of Matrix Multipliers for Normalized Frame Multi-Wavelets and Applications in Engineering Material Technology

2013 ◽  
Vol 753-755 ◽  
pp. 2321-2324
Author(s):  
Yong Fan Xu
Keyword(s):  
Fourier Multipliers ◽  
Frame Theory ◽  
Constructive Method ◽  
Sufficient Condition ◽  
Engineering Material ◽  
Material Technology ◽  
Decomposition Scheme ◽  
Affine Frames ◽  
Active Research

Frame theory has been the focus of active research for twenty years, both in theory and applications. Matrix Fourier multipliers send every orthonoamal wavelet to an orthonoamal wavelet. In this work, the notion of the bivariate generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of bivariate affine pseudoframes for subspaces is investigated. The construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a BGMS is established.

The Characters of Multiple Tight Multivariate Wavelet Frames and Application in Quantum Physics

2012 ◽  
Vol 459 ◽  
pp. 271-274
Author(s):  
De Lin Hua ◽  
Qing Bin Lu
Keyword(s):  
Quantum Physics ◽  
Materials Science ◽  
Constructive Method ◽  
Tight Frames ◽  
Wavelet Frames ◽  
Science And Engineering ◽  
Interdisciplinary Field

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. This paper is devoted to the study and construction of finitely supported tight multivariate frames of multivariate multi-wavelets. Inparticular, a necessary conditi- on for their existence is obtained to present some feasible idea for designing such MRA tight frames. The characteristics of binary multiscale pseudoframes for subspaces is investigated. The constructi- on of a GMS of Paley-Wiener subspace of is studied. A constructive method for affine multivariate frames based on such a GMS is established.

The Characteristics of Affine Bivariate Pseudoframes of Subspace Associated with a Bivariate Filter Functions

2010 ◽  
Vol 439-440 ◽  
pp. 926-931
Author(s):  
Yu Min Yu
Keyword(s):  
Frame Theory ◽  
Constructive Method ◽  
Sufficient Condition ◽  
Decomposition Scheme ◽  
Affine Frames ◽  
Active Research

Frame theory has been the focus of active research for twenty years, both in theory and applications. In this work, the notion of the bivariate generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of bivariate affine pseudoframes for subspaces is investigated. The construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a BGMS is established.

The Description and Characterization of Symmetric Frames and Gabor Frames and Applications in Material Engineering

2013 ◽  
Vol 712-715 ◽  
pp. 2458-2463
Author(s):  
Qing Jiang Chen ◽  
Xiao Ting Lei ◽  
Jian Feng Zhou
Keyword(s):  
Legendre Polynomials ◽  
Materials Science ◽  
Tight Frame ◽  
Simple Approach ◽  
Gabor Frames ◽  
Wavelet Frames ◽  
Science And Engineering ◽  
Interdisciplinary Field ◽  
Frame Wavelets

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this paper, we discuss a new set of symmetric tight frame wave-lets with the associated filterbanks outputs downsampled by several generators. The frames consist of several generators obtained from the lowpass filter using spectral factorization, with lowpass fil-ter via a simple approach using Legendre polynomials. The filters are feasible to be designed and offer smooth scaling functions and frame wavelets. We shall give an example to demonstrste that so -me examples of symmetric tight wavelet frames with three compactly supported real-valued sym- metric generators will be presented to illustrate the results.

The Features of Multiscale Pseudoframes and Gabor Frames According to Bivariate Filter Functions

2012 ◽  
Vol 424-425 ◽  
pp. 106-110 ◽  
Author(s):  
Zhong Yin Chen ◽  
Jin Shun Feng
Keyword(s):  
Frequency Analysis ◽  
Dimensional Space ◽  
Frame Analysis ◽  
Gabor Frames ◽  
Constructive Method ◽  
Sufficient Condition ◽  
Wavelet Theory ◽  
Dual Frames ◽  
Time Frequency ◽  
Decomposition Scheme

The advantages of wavelet analysis and their promising featu-res in various application have attracted a lot of interest and effort in re-cent years. Frame analysis has become popular much later in sampling theory, time-frequency analysis and wavelet theory. In this work, the notion of the binary generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of binary multiscale pseudof-rames for subspaces is investigated. The construction of a BGMS of Paley-Wiener subspace ofis studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a BGMS is established. A method for designing a class of affine bivariate dual frames in bi-dimensional space is presented. The results we obtain gains much improvement.

The Excellent Traits of a Class of Orthogonal Quarternary Wavelet Wraps with Short Support

2011 ◽  
Vol 219-220 ◽  
pp. 496-499
Author(s):  
Guo Xin Wang ◽  
De Lin Hua
Keyword(s):  
Functional Analysis ◽  
Multiresolution Analysis ◽  
Frame Theory ◽  
Constructive Method ◽  
Sufficient Condition ◽  
Analysis Method ◽  
Orthogonal Wavelet ◽  
Decomposition Scheme ◽  
Novel Approach ◽  
Generalized Multiresolution Analysis

The frame theory has been one of powerful tools for researching into wavelets. In this article, the notion of orthogonal nonseparable quarternary wavelet wraps, which is the generalizati- -on of orthogonal univariate wavelet wraps, is presented. A novel approach for constructing them is presented by iteration method and functional analysis method. A liable approach for constructing two-directional orthogonal wavelet wraps is developed. The orthogonality property of quarternary wavelet wraps is discussed. Three orthogonality formulas concerning these wavelet wraps are estabished. A constructive method for affine frames of L2(R4) is proposed. The sufficient condition for the existence of a class of affine pseudoframes with filter banks is obtained by virtue of a generalized multiresolution analysis. The pyramid decomposition scheme is established based on such a generalized multiresolution structure.

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