Sobolev空间Hs(R)中框架的必要条件

吉林大学学报(理学版)

Sobolev空间H^s(R)中框架的必要条件

张建平

北京工业大学应用数理学院, 北京 100124; 榆林学院数学与统计学院, 陕西榆林 719000

收稿日期:2016-03-25 出版日期:2017-01-26 发布日期:2017-02-02
通讯作者: 张建平 E-mail:zhjp198254@163.com

Necessary Conditions for Frames in Sobolev Space H^s(R)

ZHANG Jianping

College of Applied Sciences, Beijing University of Technology, Beijing 100124, China;School of Mathematics and Statistics, Yulin University, Yulin 719000, Shaanxi Province, China

Received:2016-03-25 Online:2017-01-26 Published:2017-02-02
Contact: ZHANG Jianping E-mail:zhjp198254@163.com

摘要/Abstract

摘要： 利用时频分析方法和Plancherel定理, 得到Sobolev空间中小波系与Gabor系各自作成框架的必要条件, 从而将L²(R)空间中的结果推广到Sobolev空间中, 丰富了Sobolev空间中框架的相关理论.

关键词: 小波框架, Gabor框架, Sobolev空间

Abstract: By using the timefrequency analysis method and the Plancherel theorem, the author obtained necessary conditions for wavelet and Gabor systems
which could be made frames in Sobolev space, respectively. This generalized some results in L²(L) to Sobolev space, and enriched the related theory about the frames in Sobolev space.

Key words: Sobolev space, Gabor frame, wavelet frame

中图分类号:

O174.2

张建平. Sobolev空间H^s(R)中框架的必要条件[J]. 吉林大学学报(理学版), 2017, 55(01): 55-60.

ZHANG Jianping. Necessary Conditions for Frames in Sobolev Space H^s(R)[J]. Journal of Jilin University Science Edition, 2017, 55(01): 55-60.

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