Sobolev空间H^s(R)中框架的必要条件  

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

作　　者：张建平[1,2] 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)

机构地区：[1]北京工业大学应用数理学院,北京100124 [2]榆林学院数学与统计学院,陕西榆林719000

出　　处：《吉林大学学报（理学版）》2017年第1期55-60,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11271037)

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.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（R ） to Sobolev space, and enriched the related theory about the frames in Sobolev space.

关 键 词：小波框架 GABOR框架 SOBOLEV空间 

分 类 号：O174.2[理学—数学]