Additive stability of frames

被引：0
|
作者：
Asipchuk, Oleg [1 ]
Glidewell, Jacob [2 ]
Rodriguez, Luis [1 ]
机构：
[1] Florida Int Univ, Dept Math & Stat, Miami, FL 33199 USA
[2] Indiana Univ, Dept Math, Bloomington, IN 47405 USA
来源：
SAMPLING THEORY SIGNAL PROCESSING AND DATA ANALYSIS | 2024年 / 22卷 / 02期
关键词：
Frames; Frame Theory; Stability; Stability of frames; GABOR FRAMES;
D O I：
10.1007/s43670-024-00094-w
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Given a frame in a finite dimensional Hilbert space we construct additive perturbations which decrease the condition number of the frame. By iterating this perturbation, we introduce an algorithm that produces a tight frame in a finite number of steps. Additionally, we give sharp bounds on additive perturbations which preserve frames and we study the effect of appending and erasing vectors to a given tight frame. We also discuss under which conditions our finite-dimensional results are extendable to infinite-dimensional Hilbert spaces.
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页数：16
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