Characterization of Compact Support of Fourier Transform for Orthonormal Wavelets of L^2（R^d） Characterization of Compact Support of Fourier Transform for Orthonormal Wavelets of L 2(R d)期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Characterization of Compact Support of Fourier Transform for Orthonormal Wavelets of L^2（R^d）

摘要：

Let{ψμ} be an orthonormal wavelet of L^2（R^d） and the support of a whole of its Fourier transform be Uμsupp{ψμ}=Пi=1^dAi, Di]-Пi=1^d（Bi, Ci）, Ai≤Bi≤Ci≤Di. Under the weakest condition that each │ψμ│, is continuous for ω ∈ δ（Пi=1^dAi, Di]）, a characterization of the above support of a whole is given.

关键词：

正交微波多解分析尺度函数紧支柱

收稿时间：

2001-08-08

修稿时间：

2001-08-082002-04-01

Characterization of Compact Support of Fourier Transform for Orthonormal Wavelets of L 2(R d)

Authors:

Zhi Hua Zhang

Institution:

(1) Department of Mathematics, University of California, Davis, California 95616, USA

Abstract:

Let {ψ_μ} be an orthonormal wavelet of L ²(R ^d) and the support of a whole of its Fourier transform be

${\bigcup\limits_\mu {{\text{supp}}{\left\{ {\hat{\psi }_{\mu } } \right\}}} } = {\prod\limits_{i = 1}^d {{\left {A_{i} ,D_{i} } \right]}} } - {\prod\limits_{i = 1}^d {{\left( {B_{i} ,C_{i} } \right)}} },A_{i} \leqslant B_{i} \leqslant C_{i} \leqslant D_{i} .$

Under the weakest condition that each ${\left| {\hat{\psi }_{\mu } } \right|}$ is continuous for $w \in \partial {\left( {{\prod\nolimits_{i = 1}^d {{\left {A_{i} ,D_{i} } \right]}} }} \right)},$ a characterization of the above support of a whole is given.

Keywords:

Orthonormal wavelets Multiresolution analysis Scaling function Compact support

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