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K-g-框架与斜对偶 被引量：1

K-g-frames and oblique duality
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摘要 在Hilbert空间中定义了K-g-框架,探讨K-g-框架与g-框架的一些本质差别,并对K-g-框架加以刻画.此外,将斜对偶原则应用到K-g-框架上,研究斜对偶K-g-框架分解中涉及的两个框架可交换的充分条件以及斜对偶K-g-框架分解的等价刻画. In this paper, K-g -frames are introduced. We study the essential distinctions between K-g -frames and g -frames, and then give the new characterizations of K-g -frames. Futhermore, applying oblique principles to K - g - frames, we get a sufficient condition for a pair of oblique dual K - g - frames to be symmetric and characterize the decomposition of oblique dual K - g - frames.
作者 周燕
机构地区 福州大学数学与计算机科学学院
出处 《福州大学学报（自然科学版）》 CAS CSCD 北大核心 2014年第1期25-28,34,共5页 Journal of Fuzhou University(Natural Science Edition)
基金 天元基金资助项目(11226099) 福建省自然科学基金资助项目(2013J05004) 福州大学科技发展基金资助项目(2012-XY-21 2012-XQ-29 2013-XQ-33) 福州大学科研启动基金资助项目(022410)
关键词 K-框架 K—g-框架 斜对偶 K - frames K - g - frames oblique duality
分类号 O177.1 [理学—基础数学]
  • 相关文献

参考文献15

  • 1Sun W C. G- frames and g- Riesz bases [ J ]. Math Anal Appl, 2006, 322 (1) : 437 -452.
  • 2Gavruta P. Frames for operators[J]. Appl Comput Harmon Anal, 2012, 32:139 -144.
  • 3Gavruta P. On the duality of fusion frames [ J]. Math Anal Appl, 2007, 333 (2) : 871 -879.
  • 4Christensen O, Goh S S. Pairs of oblique duals in spaces of periodic functions[ J]. Adv Comput Math, 2010, 32:353 -379.
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  • 7Eldar Y C. Sampling with arbitrary sampling and reconstruction spaces and oblique dual frames[ J]. Fourier Anal Appl, 2003, 9(1) : 77 -96. Christensen O, Eldar Y C. Oblique dual frames and shift - invariant spaces [ J ]. Appl Comput Harmon Anal, 2004, 17 : 48 - 68. Eldar Y C, Werther T. General framework for consistent sampling in Hilbert spaces[ J]. Int Wavelets Multi Inf Pro, 2005, 3 ( 3 ) : 347 - 359.
  • 8Eldar Y C. Sampling with arbitrary sampling and reconstruction spaces and oblique dual frames[ J]. Fourier Anal Appl, 2003, 9(1) : 77 -96.
  • 9Christensen O, Eldar Y C. Oblique dual frames and shift - invariant spaces [ J ]. Appl Comput Harmon Anal, 2004, 17 : 48 - 68.
  • 10Eldar Y C, Werther T. General framework for consistent sampling in Hilbert spaces[ J]. Int Wavelets Multi Inf Pro, 2005, 3 ( 3 ) : 347 - 359.

二级参考文献33

  • 1Duffin, R. J., Schaeffer, A. C.: A class of nonharmonic Fourier series. Trans. Amer. Math. Soc., 72, 341-366 (1952)
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  • 10Sun, W.: Stability of g-frames. J. Math. Anal. Appl., 326(2), 858-868 (2007)

共引文献43

同被引文献12

  • 1DUFFIN R J,SCHAEFFER A C. A class of nonharmonic Fourier series[J]. Trans Math Soc,1952,72:341 -366.
  • 2DAUBECHIES I,GROSSMANbt A, MEYER Y. Painless nonorthogonal expansions [ J ]. J Math Phys, 1986,27 : 1271 - 1283.
  • 3CASAZZA P G. The art of frame theory [J]. Taiwannese J Math,2000,4(2) :129 -201.
  • 4CHRISTENSEN O. An introuduction to frames and Riesz bases [ M]. Boston: Birkhiuser,2003.
  • 5GAVRUTA L. Frames for operators[J]. Appl. Comp. Harm. Anan.,2012 ,32 :139 - 144.
  • 6SUN W C. g - frames and g - Riesz bases [ J]. J. Math. Anal. Appl.,2006,322 ( 1 ) :437 - 452.
  • 7GAVRUTA P. Frames for operators [J]. Appl Comput Harmon Anal,2012,32:139 - 144.
  • 8Christensen O. An introuduction to frames and Riesz bases [ M]. Boston: Birkhluser,2003.
  • 9DOUGLAS R G. On majorization, factorization and range inclusion of operators on Hilbert Space [ J ]. Proc, Amer, Math, Soc,1996,17(2) :413 -415.
  • 10CHRISTENSEN O. Frames and pseudo - inverse[ J ]. Math Anal Appl , 1995,191 : 401 - 414.

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福州大学学报（自然科学版）
2014年 第1期

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