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Holmes R.B. and Paulsen V.I. (2004) Optimal frames for erasures. Linear Algebra and Its Applications, 377, 31-51.

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

  作者: 李亮, 李鹏同

  关键字: K-框架, 最佳K-对偶, 丢失K-frame, Optimal K-dual, Erasure

  期刊名称: 《Advances in Applied Mathematics》, Vol.3 No.4, 2014-11-20

  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.