华东师范大学学报(自然科学版) ›› 2006, Vol. 2006 ›› Issue (3): 44-50.

• 数学 统计学 • 上一篇    下一篇

关于非扩展矩阵小波的存在性

郭凤晨

  

  1. 华东师范大学 数学系, 上海 200062
  • 收稿日期:2004-07-07 修回日期:2004-11-17 出版日期:2006-05-25 发布日期:2006-05-25
  • 通讯作者: 郭凤晨

On the Existence of Wavelets for Non-Expansive Dilation Matrices(Chinese)

GUO Feng-chen   

  1. Department of Mathematics, East China Normal University, Shanghai 200062, China
  • Received:2004-07-07 Revised:2004-11-17 Online:2006-05-25 Published:2006-05-25
  • Contact: GUO Feng-chen

摘要： 用D表示n阶可逆实矩阵的集合,Γ表示Rn中的点集.小波分析的一个基本问题是对什么样的(D,Γ)存在小波.本文证明了当D={Aj,j∈Z}, A是n阶实矩阵, 满足A是对角矩阵块时, 存在(D,Zn)小波. 其中, A1是扩展矩阵,A2是行列式不为零的幂等阵.

关键词: 小波格, 扩展矩阵, 小波格, 扩展矩阵

Abstract: Let D be a collection of invertible n×n real matrices and Γ a collection of points in Rn. this paper proved that when D={Aj,j∈Z}, A is a real n×n matrix, such that
A be diagonal matrix with submatrices us its elemets, where A1 is expansive, A2 is idempotent with det A2≠0, then there exists a (D,Γ) wavelet.

Key words: FONT-FAMILY: 宋体, mso-bidi-font-family: 'Times New Roman', mso-font-kerning: 1.0pt, mso-ansi-language: VI, mso-fareast-language: ZH-CN, (D, FONT-FAMILY: 宋体, mso-bidi-font-family: 'Times New Roman', mso-font-kerning: 1.0pt, mso-ansi-language: VI, mso-fareast-language: ZH-CN

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