AAM  >> Vol. 3 No. 4 (November 2014)

    Parseval K-框架的1-丢失最佳K-对偶
    The Optimal K-Duals for 1-Erasure for Parseval K-Frames

  • 全文下载: PDF(463KB) HTML    PP.192-200   DOI: 10.12677/AAM.2014.34028  
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作者:  

李 亮,李鹏同:南京航空航天大学,数学系,南京

关键词:
K-框架最佳K-对偶丢失K-frame Optimal K-dual Erasure

摘要:

本文引入K-对偶的概念,对有限维Hilbert空间的Parseval K-框架,利用K-对偶来研究在丢失意义下的最佳 K-对偶。本文讨论了Parseval K-框架的典则K-对偶是唯一最佳K-对偶的充分必要条件。并讨论了在某些特殊条件下典则K-对偶不是最佳K-对偶或者不是唯一的最佳K-对偶。

In this paper, we introduce the concept of K-dual. We investigate the K-duals that are optimal for erasures for Parseval K-frames in finite Hilbert spaces. We will give the necessary and sufficient conditions under which the canonical K-dual is the unique optimal K-duals for erasures. We also discuss some special conditions under which the canonical K-dual is not the optimal K-dual or op-timal K-dual but not the unique one.

文章引用:
李亮, 李鹏同. Parseval K-框架的1-丢失最佳K-对偶[J]. 应用数学进展, 2014, 3(4): 192-200. http://dx.doi.org/10.12677/AAM.2014.34028

参考文献

[1] Casazza, P.G. and Kovačević, J. (2003) Equal-Norm tight frames with erasures. Advances in Computational Mathematics, 18, 387-430.
[2] Goyal, V.K., Kovačević J. and Kelner, J.A. (2001) Quantized frame expansions with erasures. Applied and Computational Harmonic Analysis, 10, 203-233.
[3] Holmes R.B. and Paulsen V.I. (2004) Optimal frames for erasures. Linear Algebra and Its Applications, 377, 31-51.
[4] Lopez, J.S. and Han, D.G. (2010) Optimal dual frames for erasures. Linear Algebra and Its Applications, 432, 471-482.
[5] Leng, J.S. and Han D.G. (2011) Optimal dual frames for erasures II. Linear Algebra and Its Applications, 435, 1464- 1472.
[6] Christensen, O. (2003) An introduction to frames and riesz bases. Birkhauser, Boston.
[7] Han, D.G. and Larson D.R. (2000) Frames, bases and group representations. Memoirs of the American Mathematical Society, 697, 1-94.
[8] Gǎvruta, L. (2012) Frames for operators. Applied and Computational Harmonic Analysis, 32, 139-144.
[9] Xiao, X.C., Zhu, Y.C. and Gavruta, L. (2013) Some properties of K-frames in Hilbert spaces. Results in Mathematics, 63, 1243-1255.
[10] 丁明玲, 肖祥春, 曾晓明 (2013) Hilbert空间中的紧K-框架. 数学学报, 56, 105-112.
[11] Christensen, O. (1995) Frames and pseu-do-inverse. The Journal of Mathematical Analysis and Applications, 195, 401- 414.