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A SUFFICIENT CONDITION FOR AFFINE FRAMES WITH MATRIX DILATION 被引量:1
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作者 Dengfeng Li Xianliang Shi 《Analysis in Theory and Applications》 2009年第2期166-174,共9页
A sufficient condition for affine frame with an arbitrary matrix dilation is presented. It is based on the univariate case by Shi, and generalizes the univariate results of Shi, Casazza and Christensen from one dimens... A sufficient condition for affine frame with an arbitrary matrix dilation is presented. It is based on the univariate case by Shi, and generalizes the univariate results of Shi, Casazza and Christensen from one dimension with an arbitrary real number a (a 〉 1) dilation to higher dimension with an arbitrary expansive matrix dilation. 展开更多
关键词 FRAME WAVELET affine frame expansive matrix dilation
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Homogeneous Approximation Property for Wavelet Frames with Matrix Dilations,Ⅱ 被引量:1
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作者 Zhi Jing ZHAO Wen Chang SUN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第1期183-192,共10页
The homogeneous approximation property (HAP) states that the number of building blocks involved in a reconstruction of a function up to some error is essentially invariant under time-scale shifts. In this paper, we ... The homogeneous approximation property (HAP) states that the number of building blocks involved in a reconstruction of a function up to some error is essentially invariant under time-scale shifts. In this paper, we show that every wavelet frame with nice wavelet function and arbitrary expansive dilation matrix possesses the HAP. Our results improve some known ones. 展开更多
关键词 Wavelet frames homogeneous approximation property HAP matrix dilations
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Construction of Multivariate Tight Framelet Packets Associated with Dilation Matrix
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作者 Firdous A.Shah Abdullah 《Analysis in Theory and Applications》 CSCD 2015年第2期109-122,共14页
In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles. We also prove how to construct various tight fra... In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles. We also prove how to construct various tight frames for L2 (JRa) by replacing some mother framelets. 展开更多
关键词 WAVELET tight frame framelet packet matrix dilation extension principle Fouriertransform.
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A Property of MRA of Multiplicity r with an Arbitrary Dilation Matrix
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作者 楚冰 薛明志 李登峰 《Chinese Quarterly Journal of Mathematics》 CSCD 1999年第3期92-95, ,共4页
In this paper, we give a property for multivariate multiresolution analysis of multiplicity r with an arbitrary dilatiion matrix.
关键词 multiresolution analysis orthonormal basis dilation matrix
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Construction of periodic wavelet frames with dilation matrix 被引量:2
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作者 Dayong LU Dengfeng LI 《Frontiers of Mathematics in China》 SCIE CSCD 2014年第1期111-134,共24页
An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito [Appl. Comput. Harmon. Anal., 2008, 125: 68-186]. We exten... An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito [Appl. Comput. Harmon. Anal., 2008, 125: 68-186]. We extend their results to the dilation matrix cases in two aspects. We first show that the periodization of any wavelet frame constructed by the unitary extension principle formulated by Ron and Shen is still a periodic wavelet frame under weaker conditions than that given by Zhang and Saito, and then prove that the periodization of those generated by the mixed extension principle is also a periodic wavelet frame if the scaling functions have compact supports. 展开更多
关键词 Periodic wavelet frames extension principle matrix dilation function periodization
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A NOTE ON FINITE ELEMENT WAVELETS
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作者 谌秋辉 陈翰麟 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2001年第4期517-525,共9页
The refinability and approximation order of finite element multi-scale vector are discussed in [1]. But the coefficients in the conditions of approximation order of finite element multi-scale vector are incorrect ther... The refinability and approximation order of finite element multi-scale vector are discussed in [1]. But the coefficients in the conditions of approximation order of finite element multi-scale vector are incorrect there. The main purpose of this note is to make a correction of the error in the main result of [1]. These Cuefficients are very important for the properties of wavelets, such as vanishing moments and regularity. 展开更多
关键词 Approximation order SYMBOL multi-scale vector matrix dilation equation
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