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g-Besselian Frames in Hilbert Spaces 被引量：11

g-Besselian Frames in Hilbert Spaces
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摘要 In this paper, we introduce the concept of a g-Besselian frame in a Hilbert space and discuss the relations between a g-Besselian frame and a Besselian frame. We also give some characterizations of g-Besselian frames. In the end of this paper, we discuss the stability of g-Besselian frames. Our results show that the relations and the characterizations between a g-Besselian frame and a Besselian frame are different from the corresponding results of g-frames and frames. In this paper, we introduce the concept of a g-Besselian frame in a Hilbert space and discuss the relations between a g-Besselian frame and a Besselian frame. We also give some characterizations of g-Besselian frames. In the end of this paper, we discuss the stability of g-Besselian frames. Our results show that the relations and the characterizations between a g-Besselian frame and a Besselian frame are different from the corresponding results of g-frames and frames.
作者 Ming Ling DING Yu Can ZHU
机构地区 College of Computer and Information Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2010年第11期2117-2130,共14页 数学学报（英文版）
基金 Supported by Natural Science Foundation of Fujian Province,China (Grant Nos.2009J01007,2008J0183) the Education Commission Foundation of Fujian Province,China (Grant No.JA08013) the Science Foundation for the Youth Scholars of Fujian Agriculture and Forestry University,China (Grant No.07B23)
关键词 G-FRAME Besselian frame g-Besselian frame STABILITY g-frame, Besselian frame, g-Besselian frame, stability
分类号 O177.1 [理学—基础数学] O1-19 [理学—基础数学]
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参考文献22

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同被引文献54

  • 1郑志鹏.τ粒子质量的最新数据[J].物理,1993,22(1):1-3. 被引量：1
  • 2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
  • 3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
  • 4DUFFIN R J, SCHAEFFER A C. A class of nonharmonic Fourier series[J]. Trans Amer Math Soc, 1952,72:341 -366.
  • 5DAUBECHIES I, GROSSMANN A, MEYER Y. Painless nonorthogonal expansions[J]. J Math Phys, 1986,27:1271 - 1283.
  • 6CASAZZA P G. The art of frame theory [ J ]. Taiwan Residents J of Math, 2000,4 (2) :129 -201.
  • 7CHRISTENSEN O. An Introduction to Frames and Riesz Bases[ M]. Boston: Birkhauser, 2003.
  • 8SUN W C. G-frames and g-Riesz bases[J]. J Math Anal Appl, 2006,322( 1 ) :437 -452.
  • 9SUN W C. Stability of g-frames[J]. J Math Anal Appl, 2006,326(2) :858 -868.
  • 10LI D F, SUN W C. Some equalities and inequalities for generalized frames[J]. Chin Jour of Contemp Math, 2008,29(3) : 301 - 308.

引证文献11

二级引证文献15

Acta Mathematica Sinica,English Series
2010年 第11期

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