Consistent Sampling Approximations in Abstract Hilbert Spaces

被引：0
|
作者：
Kang, Sinuk [1 ]
Kwon, Kil Hyun [1 ]
Lee, Dae Gwan [2 ]
机构：
[1] Korea Adv Inst Sci & Technol, Dept Math Sci, Daejeon 34141, South Korea
[2] Kumoh Natl Inst Technol, Dept Math & Big Data Sci, Gumi 39177, South Korea
来源：
AXIOMS | 2024年 / 13卷 / 07期
基金：
新加坡国家研究基金会;
关键词：
consistent sampling; generalized sampling; oblique projection; frame;
D O I：
10.3390/axioms13070489
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper considers generalized consistent sampling and reconstruction processes in an abstract separable Hilbert space. Using an operator-theoretical approach, quasi-consistent and consistent approximations with optimal properties, such as possessing the minimum norm or being closest to the original vector, are derived. The results are illustrated with several examples.
引用
收藏
页数：11
相关论文
共 50 条
12345