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Biorthogonal multiple wavelets generated by vector refinement equation

Science China Mathematics 2007年第7期50卷 1015-1025页

作者： Song LI~(1+) Jun XIAN~2 1 Department of Mathematics,Zhejiang University,Hangzhou 310027,China 2 Department of Mathematics,Sun Yat-Sen University,Guangzhou 510275,China 1. Department of Mathematics Zhejiang University Hangzhou 310027 China 2. Department of Mathematics Sun Yat-Sen University Guangzhou 510275 China

Biorthogonal multiple wavelets are generated from refinable function vectors by using the multiresolution analysis. In this paper we provide a general method for the construction of compactly supported biorthogonal multiple wavelets by refinable function vectors which are the solutions of vector refinement equations of the form $$\varphi (x) = \sum\limits_{\alpha \in \mathbb{Z}^s } {a(\alpha )\varphi (Mx - \alpha ), x \in \mathbb{R}^s } ,$$ where the vector of functions ? = (? 1, …, ? r)T is in $(L_2 (\mathbb{R}^s ))^r ,a = :(a(\alpha ))_{\alpha \in \mathbb{Z}^s } $ is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix such that lim n→∞ M ?n = 0. Our characterizations are in the general setting and the main results of this paper are the real extensions of some known results.

关键词： refinement equation biorthogonal multiple wavelets refinable function vector 42C40 41A10 41A15 41a25

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Jackson type theorems on complex curves

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Science China Mathematics 2009年第3期52卷 493-506页

作者： TU TianLiang Deptartment of Mathematics and Informatics, North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450011, China Deptartment of Mathematics and Informatics North China Institute of Water Conservancy and Hydroelectric Power Zhengzhou 450011 China

Let Γ be a closed smooth Jordan curve in the complex plane. In this paper, with the help of a class of fundamental functions of Hermite interpolation, the author introduces a continuous function interpolation which uniformly approximates to f(z) ∈ C(Γ ) with the same order of approximation as that in Jackson Theorem 1 on real interval [1, 1]. The accuracy of the order of approximation is proved. Using the method different from the early works, the author studies simultaneous approximation to function and its derivatives and the desired results analogues to that in Jackson Theorem 2 on real interval [1, 1] are obtained.

关键词： complex curves interpolation uniform approximation order of approximation 30E05 30E10 41A05 41a25 41A28

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