尺度函数的两个性质

数学季刊 ›› 2004, Vol. 19 ›› Issue (2): 188-191.

尺度函数的两个性质

College of Science, Wuhan University of Technology, Wuhan 430063, China; Department of Basic Courses, Henan Judicial Police Vocational College, Luohe 473000, China

收稿日期:2002-10-21 出版日期:2004-06-30 发布日期:2024-03-20
作者简介:WU Hua-an(1954-),male,native of Wuhan,Hubei,an associate professor of Wuhan University of Technology,M.S.D.,engages in algebraic topology;ZHANG Gui-zhen(1963-),female,native of Luohe,Henan, a lecturer of Henan Judicial Police Vocational College,engages in basic mathematics.

Notes on the Scaling Function

College of Science, Wuhan University of Technology, Wuhan 430063, China; Department of Basic Courses, Henan Judicial Police Vocational College, Luohe 473000, China

Received:2002-10-21 Online:2004-06-30 Published:2024-03-20
About author:WU Hua-an(1954-),male,native of Wuhan,Hubei,an associate professor of Wuhan University of Technology,M.S.D.,engages in algebraic topology;ZHANG Gui-zhen(1963-),female,native of Luohe,Henan, a lecturer of Henan Judicial Police Vocational College,engages in basic mathematics.

摘要/Abstract

摘要： Two properties are given in this paper about the scaling function: suppose V_j; j ∈ Z is a multiresolution analysis with a continuous scaling function φ which have compact support set and that φ the Fourier transform of φ is a continuous real function, compactly supported, then φ(0) ≠ 0 and when supp φ = [a₁,b₁]∪[a₂,b₂](b₁ < a₂,0 < a₂), then we havea1 ≤ 0, 0 < b₁, a₁ < b₂/2 ≤ b₁, 2π < b₂ - a₁ ≤ 8π.

关键词: multiresolution , analysis, scaling , function, Fourier , transform

Abstract: Two properties are given in this paper about the scaling function: suppose V_j; j ∈ Z is a multiresolution analysis with a continuous scaling function φ which have compact support set and that φ the Fourier transform of φ is a continuous real function, compactly supported, then φ(0) ≠ 0 and when supp φ = [a₁,b₁]∪[a₂,b₂](b₁ < a₂,0 < a₂), then we havea1 ≤ 0, 0 < b₁, a₁ < b₂/2 ≤ b₁, 2π < b₂ - a₁ ≤ 8π.

Key words: multiresolution , analysis, scaling , function, Fourier , transform

中图分类号:

O175

吴华安, 张桂贞. 尺度函数的两个性质[J]. 数学季刊, 2004, 19(2): 188-191.

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