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.