Parseval K-框架的1-丢失最佳K-对偶
The Optimal K-Duals for 1-Erasure for Parseval K-Frames
DOI: 10.12677/AAM.2014.34028, PDF, HTML,  被引量 下载: 3,012  浏览: 9,814  科研立项经费支持
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。
Abstract: 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

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