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Hilbert空间中的无冗g-框架 被引量:3

Exact g-frames in Hilbert spaces
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摘要 给出Hilbert空间中无冗g-框架的一些刻画,并讨论无冗g-框架和无冗框架的关系.最后讨论无冗g-框架的扰动性. In this paper, we give some characterizations of exact g -frames in a Hilbert space,and also discuss the relations of exact g - frames and exact frames. Lastly we consider the stability of exact g -frames under perturbation.
出处 《福州大学学报(自然科学版)》 CAS CSCD 北大核心 2010年第4期461-467,共7页 Journal of Fuzhou University(Natural Science Edition)
基金 福建省自然科学基金资助项目(2009J01007 2008J0183) 福建省教育厅科研资助项目(JA08013) 福建农林大学青年教师科研基金资助项目(07B23)
关键词 HILBERT空间 无冗框架 扰动性 Hilbert spaces exact frame perturbation
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参考文献12

  • 1Duffin R J, Schaeffer A C. A class of nonharmonic Fourier series[J]. Trans Amer Math Soe, 1952, 72:341 -366.
  • 2Daubechies I, Grossmann A, Meyer Y. Painless nonorthogonal expansions[J]. J Math Phys, 1986, 27:1 271 -1 283.
  • 3Casazza P G. The art of frame theory[J]. Taiwan Residents J of Math, 2000, 4(2) : 129 -201.
  • 4Christensen O. An introduction to frames and Riesz bases [ M ]. Boston: Birkhauser, 2003.
  • 5Sun W. G-frames and g- Riesz bases[J]. J Math Anal Appl, 2006, 322(1) : 437 -452.
  • 6Sun W. Stability of g-frames[J]. J Math Anal Appl, 2006, 326(2) : 858 -868.
  • 7丁明玲,朱玉灿.g-框架的稳定性[J].福州大学学报(自然科学版),2007,35(3):321-325. 被引量:10
  • 8肖祥春,朱玉灿,王燕津,丁明玲.由g-Bessel序列定义的线性算子的一些性质[J].福州大学学报(自然科学版),2007,35(3):326-330. 被引量:6
  • 9Zhu Y C. Characterization of g - frames and g - Riesz bases in Hilbert spaces [ J ]. Aeta Mathematica Sinica: English Series, 2008, 24(10) : 1 727 - 1 736.
  • 10Xiao X C, Zhu Y C, Zeng X M. Some properties of g - Parseval frames in Hilbert spaces [ J ]. Acta Mathematica Sinica, Chi- nese Series, 2008, 51(6) : 1 143 -1 150.

二级参考文献18

  • 1Sun W.Stability of g-frames[J].J Math Anal Appl,2007,326(2):858 -868.
  • 2Casazza P G,Christensen O.Perturbation of operators and applications to frame theory[J].J Fourier Anal Appl,1997,3:543-557.
  • 3Duffin R J,Schaeffer A C.A class of nonharmonic Fourier series[J].Trans Math Soc,1952(72):341-366.
  • 4Daubechies I,Grossmann A,Meyer Y.Painless nonorthogonal expansions[J].J Math Phys,1986 (27):1271-1283.
  • 5Christensen O.An introduction to frames and Riesz bases[M].Boston:Birkhǎuser,2003.
  • 6Casazza P G.The art of frame theory[J].Taiwan Residents J of Math,2000,4(2):129-201.
  • 7Ferreira PJSG.Mathematics for multimedia signal processing Ⅱ:discrete finite frames and signal reconstruction[C]//Byrnes J S.Signal Processing for Multimedia.Amsterdam:IOS Press,1999:35-54.
  • 8Chan R H,Riemenschneider S D,Shen L,et al.Tight frame:an efficient way for high -resolution image reconstruction[J].Comput Harmon Anal,2004(17):91-115.
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  • 10Sun W.G-frames and g-Riesz bases[J],J Math Anal Appl,2006(322):437-452.

共引文献10

同被引文献34

  • 1丁明玲,朱玉灿.g-框架的稳定性[J].福州大学学报(自然科学版),2007,35(3):321-325. 被引量:10
  • 2肖祥春,朱玉灿,王燕津,丁明玲.由g-Bessel序列定义的线性算子的一些性质[J].福州大学学报(自然科学版),2007,35(3):326-330. 被引量:6
  • 3Yu Can ZHU.q-Besselian Frames in Banach Spaces[J].Acta Mathematica Sinica,English Series,2007,23(9):1707-1718. 被引量:4
  • 4Duffin R J, Schaefief A C. A class of nonharmonic Fourier series [ J ]. Transactions of the American Mathematical Society, 1952, 72(2) : 341 -366.
  • 5Daubechies I, Grossmann A, Meyer Y. Painless nonorthogonal expansions [ J]. Journal of Mathematical Physics, 1986, 27 (5) : 1271- 1283.
  • 6Sun Wen - chang. G - frames and g - Riesz bases [ J ]. Journal of Mathematical Analysis and Applications, 2006, 322 ( 1 ) : 437 - 452.
  • 7Zhu Yu - can. Characterizations of g - frames and g - Riesz bases in Hilbert spaces [ J ]. Acta Mathematica Sinica: English Serires, 2008, 24(10) : 1 727 -1 736.
  • 8Li Jian - zhen, Zhu Yu - can. Exact g - frames in Hilbert spaces [ J ]. Journal of Mathematical Analysis and Application, 2011, 374( 1 ) : 201 -209.
  • 9Casazza P G. Kutyniok G. Frame of subspaces[J]. Contemporery mathematics, 2004, 345( 1 ) : 87 -114.
  • 10Casazza P G, Kutyniok G, Li Shi - dong. Fusion frames and distributed processing[J]. Applied Computational Harmonic A- nalysis, 2008, 25(1): 114-132.

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