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Hilbert C-模中融合框架的新刻画 被引量：1

New characterization of fusion frames in Hilbert C＊-modules
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摘要 观察到Hilbert C*-模中融合框架原定义的不合理性,然后通过权重集的选取将其改进,得到融合框架的新定义并给出其等价形式.特别地,利用算子理论方法得到了Hilbert C*-模中融合框架的一个新刻画. An observation shows that the original definition of fusion frames in Hilbert C＊-modules is unrea- sonable and then, it is improved by a replacement of the associated weight set. An equivalent form of the new definition of fusion frames in Hilbert C＊-modules is also given and, especially, a new characterization of fusion frames in Hilbert C＊-modules is obtained by the method of operator theory
作者 相中启 黄时祥
机构地区 上饶师范学院数学与计算机科学学院
出处 《纯粹数学与应用数学》 2015年第5期456-463,共8页 Pure and Applied Mathematics
基金 国家自然科学基金(11271148)
关键词 HILBERT C-模 融合框架 刻画 Hilbert C＊-module, fusion frame, characterization
分类号 O174.6 [理学—基础数学]
  • 相关文献

参考文献16

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二级参考文献45

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共引文献5

同被引文献19

  • 1Duffin R J, Schaeffer A C. A class of nonharmonic Fourier series[J]. Transactions of the American Mathematical Society, 1952, 72(2) :341-366.
  • 2Daubechies I, Grossmann A, Meyer Y. Painless nonorthogonal expansions[J]. Journal of Mathematical Physics, 1986, 27 (5) : 1271- 1283.
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  • 4Christensen O. An introduction to frames and Riesz bases[M]. Boston.. Birkhauser, 2002:87-165.
  • 5Benedetto J J, Powell A, Yilmaz O. Sigma-Delta quantization and finite frames[J]. IEEE Transactions on Information Theory, 2006, 52(5):1990-2005.
  • 6Candes E J, Donoho D L. Continuous curvet transform: Ⅱ. Discretization and frames[J]. Applied and Computational Har- monic Analysis, 2005, 19(2) :198-222.
  • 7Sun W C. Asymptotic properties of Gabor frame operators as sampling density tends to infinity[J]. Journal of Functional Analysis, 2010, 258(3):913-932.
  • 8Sun W C. G-frames and g-Riesz bases[J]. Journal of Mathematical Analysis and Applications, 2006, 322(1) :437-452.
  • 9Khosravi A, Khosravi B. Fusion frames and g-frames in Hilbert C-modules[J]. International Journal of Wavelets, Multiresolution and Information Processing, 2008, 6(3):433-446.
  • 10Xiao X C, Zeng X M. Some properties of g-frames in Hilbert C -modules[J]. Journal of Mathematical Analysis and Applications, 2010, 363(2):399-408.

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纯粹数学与应用数学
2015年 第5期

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