可相位恢复p-框架的稳定性  

Stability of phase retrievable p-frames

作　　者：林丽琼[1] 张云南[2] 蔡碧琼[2] Liqiong Lin;Yunnan Zhang;Biqiong Cai

机构地区：[1]福州大学数学与统计学院,福州350108 [2]福建师范大学数学与统计学院,福州350117

出　　处：《中国科学：数学》2022年第1期51-62,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11971108)资助项目。

摘　　要：相位恢复问题在物理和工程中有着广泛的应用.设X是Banach空间,1<p<∞.设Φ={x_(n)}_(n)∈I是X上的p-框架.若对任意x^(∗);y^(∗)∈X^(∗),等式|x^(∗)(x_(n))|=|y^(∗)(x_(n))|对任意n∈I成立蕴涵存在||=1使得x^(∗)=y^(∗),则称Φ是可相位恢复的.本文证明在有限维Banach空间上,可相位恢复p-框架是稳定的,但在有Schauder基的无限维Banach空间上,可相位恢复p-框架不是稳定的.本文也说明在无限维Banach空间上,可通过有限维空间足够好的逼近来得到可相位恢复p-框架的稳定性结果.The phase retrieval problem presents itself in many applications in physics and engineering.Let X be a Banach space and 1<p<1.LetΦ=fxngn2I be a p-frame for X.We sayΦis phase retrievable,if the equalities jx^(∗)(x_(n))j=jy^(∗)(x_(n))j for every n 2 I imply that there exists j j=1 so that x^(∗)=y^(∗)for any x^(∗);y^(∗)2 X^(∗).In this paper,we prove that phase retrieval is always stable for p-frames in finite-dimensional Banach spaces and it is never uniformly stable for p-frames in an infinite-dimensional Banach space X with a Schauder basis.We establish that stable phase retrieval is possible for the elements of X^(∗)that can be approximated sufficiently well by finite-dimensional expansion.

关 键 词：BANACH空间 p-框架 相位恢复 

分 类 号：O177[理学—数学]