有限维希尔伯特空间中的循环系

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-08-25 DOI:10.1016/j.laa.2025.08.016

Ole Christensen , Navneet Redhu , Niraj K. Shukla

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引用次数: 0

摘要

推广Kalra[10]的定义，本文的目的是分析有限维Hilbert空间中的循环框架。循环框架是Aldroubi等人在[1]及以后的文章中详细介绍和分析的动力框架的一个子类；它们特别有趣，因为它们在擦除问题中具有吸引人的性质。通过应用另一种方法，我们能够揭示新的光一般动力框架以及循环框架。特别是，我们提供了动力框架的表征，这反过来又导致循环框架的表征。

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Cyclic frames in finite-dimensional Hilbert spaces

Generalizing a definition by Kalra [10], the purpose of this paper is to analyze cyclic frames in finite-dimensional Hilbert spaces. Cyclic frames form a subclass of the dynamical frames introduced and analyzed in detail by Aldroubi et al. in [1] and subsequent papers; they are particularly interesting due to their attractive properties in the context of erasure problems. By applying an alternative approach, we are able to shed new light on general dynamical frames as well as cyclic frames. In particular, we provide a characterization of dynamical frames, which in turn leads to a characterization of cyclic frames.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.