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Banach空间的框架和原子分解的摄动及其稳定性 被引量:5

Perturbation and Stability of Frames and Atomic Decompositions for Banach Spaces
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摘要 本文利用框架理论对 Banach空间的框架和原子分解的摄动及其稳定性进行了研究,改进并推广了文[5,6]的工作. Abstract In this paper, we study perturbation and stability of frames and atomic decompositions for Banach spaces by utilizing the theory of frames, and improve on and generalize the results in [5] and [6].
作者 辛杰 周家云
出处 《数学学报(中文版)》 SCIE CSCD 北大核心 2002年第6期1165-1170,共6页 Acta Mathematica Sinica:Chinese Series
基金 国家自然科学基金资助项目(19871048)
关键词 BANACH空间 框架 原子分解 摄动 稳定性 Frame Atomic decomposition Perturbation Stability
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参考文献8

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同被引文献36

  • 1Aldroubi A,Grochenig K.Nonuniform sampling and reconstruction in shift-invariant space[J].SIAM Rev,2001,43(4):585-620.
  • 2Cazassa P G,Christensen O.Purterbation of operators and applications to frame theory[J].J Fourier Anal Appl,1997,3(5):543-557.
  • 3Cazassa P G,Han D,Larson D R.Frames for Banach spaces[J].Contemp Math,1999,247:149-182.
  • 4Christensen O,Sroeva D.p-frames in separable Banach spaces[J].Adv Comput Math,2003,18(2):117-126.
  • 5Christensen O,Heil C.Perturbations of Banach frames and atomic decompositions[J].Math Nachr,1997,185:33-47.
  • 6Najati A,Faroughi M H.p-frames of subspaces in separable Hilbert spaces[J].Southest Asian Bull Math,2007,31:713-726.
  • 7Sun W.G-frames and G-Riesz bases[J].J Math Anal Appl,2006,322:437-452.
  • 8Najati A,Rahimi A,Faroughi M H.G-frames in Hilbert spaces[J].Bulletin of the Iranian Mathematical Society,2009,35(1):97-109.
  • 9Abdollahpour M R,Faroughi M H,Rahimi A.pG-frames in Banach spaces[J].Methods of Functional Analysis and Topology,2007,13(3):201-210.
  • 10Christensen O.An Introduction to Frames and Riesz Bases[M].Bosten:Birkhauser,2003.

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