Journal of Jilin University Science Edition

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Necessary Conditions for Frames in Sobolev Space Hs(R)

ZHANG Jianping   

  1. 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

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

CLC Number: 

  • O174.2