Supports of Fourier Transforms of Refinable Frame Functions and Their Applications to FMRA

Supports of Fourier Transforms of Refinable Frame Functions and Their Applications to FMRA

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摘要 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. 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.

作者 Yun-zhang LI Chun-hua HAN

机构地区 College of Applied Sciences

出处《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2012年第4期757-768,共12页 应用数学学报（英文版）

基金 Supported by Beijing Natural Science Foundation (No.1122008) the Scientific Research Common Programof Beijing Municipal Commission of Education (No.KM201110005030)

关键词 refinable function frame function refinable frame function refinable function, frame function, refinable frame function

分类号 O174.22 [理学—基础数学]

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Acta Mathematicae Applicatae Sinica

2012年第4期

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Supports of Fourier Transforms of Refinable Frame Functions and Their Applications to FMRA

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