The discretization problem for continuous frames

被引：26

作者：

Freeman, Daniel ^{[1
,2
]}

Speegle, Darrin ^{[1
]}

机构：

[1] St Louis Univ, Dept Math & Stat, St Louis, MO 63103 USA

[2] Duke Univ, Dept Math, Durham, NC 27708 USA

来源：

ADVANCES IN MATHEMATICS | 2019年 / 345卷

关键词：

Frames; Continuous frames; Coherent states; Sampling; THEOREM; SPACES;

D O I：

10.1016/j.aim.2019.01.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize when a coherent state or continuous frame for a Hilbert space may be sampled to obtain a frame, which solves the discretization problem for continuous frames. In particular, we prove that every bounded continuous frame for a Hilbert space may be sampled to obtain a frame. We give multiple applications to different classes of frames such as scalable frames and Gabor frames. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：784 / 813

页数：30

共 24 条

[1] A Lyapunov-type theorem from Kadison-Singer [J].