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G-Frames and g-Frame Sequences in Hilbert Spaces 被引量：12

G-Frames and g-Frame Sequences in Hilbert Spaces
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摘要 In this paper, we first determine the relations among the best bounds A and B of the g-frame, the g-frame operator S and the pre-frame operator Q and give a necessary and sufficient condition for a g-frame with bounds A and B in a complex Hilbert space. We also introduce the definition of a g-frame sequence and obtain a necessary and sufficient condition for a g-frame sequence with bounds A and B in a complex Hilbert space. Lastly, we consider the stability of a g-frame sequence for a complex Hilbert space under perturbation. In this paper, we first determine the relations among the best bounds A and B of the g-frame, the g-frame operator S and the pre-frame operator Q and give a necessary and sufficient condition for a g-frame with bounds A and B in a complex Hilbert space. We also introduce the definition of a g-frame sequence and obtain a necessary and sufficient condition for a g-frame sequence with bounds A and B in a complex Hilbert space. Lastly, we consider the stability of a g-frame sequence for a complex Hilbert space under perturbation.
作者 Yan Jin WANG Yu Can ZHU~(1))Department of Mathematics,Fuzhou University,Fuzhou 350002,P. R. China
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2009年第12期2093-2106,共14页 数学学报（英文版）
基金 supported by Natural Science Foundation of Fujian Province of China (No.2009J01007) Education Commission Foundation of Fujian Province of China (No.JA08013)
关键词 FRAME g-Bessel sequence G-FRAME g-frame sequence frame, g-Bessel sequence, g-frame, g-frame sequence
分类号 O177.1 [理学—基础数学]
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参考文献19

  • 1Duffin, R. J., Schaeffer, A. C.: A class of nonharmonic Fourier series. Trans. Amer. Math. Soc., 72, 341-366 (1952).
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  • 3Christensen, O.: Frames Riesz bases and discrete Gabor/wavelet expansions. Bull. Amer. Math. Soc., 38(3), 273-291 (2001).
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  • 8Christensen, O.: Operators with closed range pseudo-inverses and perturbation of frames for a subspace. Canad. Math. Bull., 42(1), 37-45 (1999).
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同被引文献58

  • 1XIAO XiangChun & ZENG XiaoMing Department of Mathematics,Xiamen University,Xiamen 361005,China.Some equalities and inequalities of g-continuous frames[J].Science China Mathematics,2010,53(10):2621-2632. 被引量：9
  • 2施咸亮,陈芳.Gabor框架的必要条件[J].中国科学（A辑）,2006,36(12):1413-1421. 被引量：5
  • 3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
  • 4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
  • 5DUFFIN R J, SCHAEFFER A C. A class of nonharmonic Fourier series[J]. Trans Amer Math Soc, 1952,72:341 -366.
  • 6DAUBECHIES I, GROSSMANN A, MEYER Y. Painless nonorthogonal expansions[J]. J Math Phys, 1986,27:1271 - 1283.
  • 7CASAZZA P G. The art of frame theory [ J ]. Taiwan Residents J of Math, 2000,4 (2) :129 -201.
  • 8CHRISTENSEN O. An Introduction to Frames and Riesz Bases[ M]. Boston: Birkhauser, 2003.
  • 9SUN W C. G-frames and g-Riesz bases[J]. J Math Anal Appl, 2006,322( 1 ) :437 -452.
  • 10SUN W C. Stability of g-frames[J]. J Math Anal Appl, 2006,326(2) :858 -868.

引证文献12

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Acta Mathematica Sinica,English Series
2009年 第12期

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