融合框架的近似斜对偶
Approximate oblique duality for fusion frames
AI总结：
针对融合框架分析重构非精确、精确对偶不可得或需改进性质的问题，提出近似斜对偶融合框架及系统概念，研究其性质、与近似斜对偶框架的关联、构造方法及可实现任意小重构误差的对偶构造方式。
摘要：
融合框架是处理海量数据或需要组合局部数据的应用场景中的便利工具。斜对偶融合框架适用于数据分析及后续重构需在希尔伯特空间的不同子空间中实现的场景。这类分析与重构过程通常并非精确的，且在某些情况下精确对偶不可得，或是有必要改进其性质。为解决这些问题，我们提出了近似斜对偶融合框架的概念，特别是近似斜对偶融合框架系统的概念。我们研究了它们的性质，给出了其与近似斜对偶框架的关联，提供了获取这类框架的方法，还展示了如何从给定的对偶构造出其他能实现任意小重构误差的对偶。
英文摘要：
Fusion frames are a convenient tool in applications where we deal with a large amount of data or when a combination of local data is needed. Oblique dual fusion frames are suitable in situations where the analysis for the data and its subsequent synthesis have to be implemented in different subspaces of a Hilbert space. These procedures of analysis and synthesis are in general not exact, and also there are circumstances where the exact dual is not available or it is necessary to improve its properties. To resolve these questions we introduce the concept of approximate oblique dual fusion frame, and in particular of approximate oblique dual fusion frame system. We study their properties. We give the relation to approximate oblique dual frames. We provide methods for obtaining them. We show how to construct other duals from a given one that give reconstructions errors as small as we want.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
