高维半正交波包框架的刻画

兰州理工大学学报 ›› 2020, Vol. 46 ›› Issue (6): 159-167.

高维半正交波包框架的刻画

陈欢^1,2, 陈清江²

1.陕西能源职业技术学院人文与教育学院, 陕西咸阳 712000;
2.西安建筑科技大学理学院, 陕西西安 710055

收稿日期:2019-09-23 出版日期:2020-12-28 发布日期:2021-01-07
作者简介:陈欢(1989-),女,陕西汉中人,硕士,讲师
基金资助:
国家自然科学基金(61403298)

Characterization for high dimensional semi-orthogonal wave packet frames

CHEN Huan^1,2, CHEN Qing-jiang²

1. School of Humanities and Education, Shaanxi Energy Institute, Xianyang 712000;
2. School of Science, Xi'an University of Architecture and Technology,Xi'an 710055

Received:2019-09-23 Online:2020-12-28 Published:2021-01-07

摘要/Abstract

摘要： 研究了空间L²(Rⁿ)上半正交波包框架的存在性,刻画了空间L²(Rⁿ)上的半正交波包框架的特征,得到了多个小波函数组成的波包系构成波包巴塞尔框架的充分必要条件,以及波包框架成为半正交框架的等价条件.

关键词: 波包框架, 半正交波包框架, 波包巴塞尔框架, 框架多分辨分析

Abstract: The existence of semi-orthogonal wave packet frames in the space of L²(Rⁿ) is studied, and the characteristics of semi-orthogonal wave packet frames in the space of L²(R²) are characterized as well. The necessary and sufficient conditions for wave packet systems composed of several wavelet functions to form wave packet Basel frames are established. The equivalent condition for the wave packet frame to be a semi-orthogonal frame is obtained as well.

Key words: wave packet frames, semi-orthogonal wave packet frames, wave packet parseval frames, frame multiresolution analysis

中图分类号:

O174.2

陈欢, 陈清江. 高维半正交波包框架的刻画[J]. 兰州理工大学学报, 2020, 46(6): 159-167.

CHEN Huan, CHEN Qing-jiang. Characterization for high dimensional semi-orthogonal wave packet frames[J]. Journal of Lanzhou University of Technology, 2020, 46(6): 159-167.