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A CRITERION FOR ORTHOGONALITY OF refinable functionS

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Applied Mathematics(A Journal of Chinese Universities) 2001年第4期16卷 397-401页

作者： BiNing HuangDaren Dept.ofMath. ZhongshanUniv.Guangzhou510275. Dept.ofMath. HangzhouTeachers＇CollegeHangzhou310012 CenterforMath.Sci. ZhejiangUniv.Hangzhou310027.

In this note, a criterion for orthonormality of refinable functions via characteristic polynomial of a matrix is given.

关键词： refinable function orthogonality Conjugate quadrature filter characteristic polynomial.

Supports of Fourier Transforms of refinable Frame functions and Their Applications to FMRA

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Acta Mathematicae Applicatae Sinica 2012年第4期28卷 757-768页

作者： Yun-zhang LI Chun-hua HAN College of Applied Sciences Beijing University of Technology

Let M be a d × d expansive matrix, and FL2（Ω） be a reducing subspace of L2（Rd）. This paper characterizes bounded measurable sets in Rd which are the supports of Fourier transforms of M-refinable frame functions. As applications, we derive the characterization of bounded measurable sets as the supports of Fourier transforms of FMRA （W-type FMRA） frame scaling functions and MRA （W-type MRA） scaling functions for FL2（Ω）, respectively. Some examples are also provided.

关键词： refinable function frame function refinable frame function

A Construction of Multiresolution Analysis on Interval

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Acta Mathematica Sinica,English Series 2007年第4期23卷 705-710页

作者： Di Rong CHEN Dao Hong XIANG Department of Mathematics and LMIB Beijing University of Areonautics and Astronautics Beijing 100083 P. R. China

We present a concrete method of constructing multiresolution analysis on interval. The method generalizes the corresponding results of Cohen, Daubechies and Vial [Appl. Comput. Harmonic Anal., 1（1993）, 54-81]. By the use of the subdivision operator, the expressions of the constructed functions are more compact. Furthermore, the method reveals more clearly some properties of multiresolution analysis with certain approximation order.

关键词： Multiresolution analysis refinable function Approximation order Subdivision operator

Construction of a class of multivariate compactly supported wavelet bases for L2（Rd）

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Frontiers of Mathematics in China 2012年第1期7卷 177-195页

作者： Fengying ZHOU Yunzhang LI College of Applied Sciences Beijing University of TechnologyBeijing 100124China

In this paper, for a given d x d we investigate the compactly supported expansive matrix M with ｜ det M｜ = 2, M-wavelets for L^2（R^d）. Starting with N a pair of compactly supported refinable functions and satisfying a mild condition, we obtain an explicit construction of a compactly supported wavelet p such that {2J/2b（Mj -k）：j E Z, k c gg} forms a Riesz basis for L2（Ra）. The （anti-）symmetry of such ~b is studied, and some examples are also provided.

关键词： Riesz basis wavelet refinable function