Frames induced by the action of continuous powers of an operator

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:478

Article

Aldroubi, A.¹  Huang, L. X.¹  Petrosyan, A.² 

[1] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

[2] Oak Ridge Natl Lab, Computat & Appl Math Grp, 1 Bethel Valley Rd, Oak Ridge, TN 37830 USA

关键词: Continuous frames;    Semi-continuous frames;    Dynamical sampling;    Discretization of continuous frames;    Frames induced by continuous;    powers of operators;   

DOI  :  10.1016/j.jmaa.2019.05.066

来源: Elsevier

【 摘 要 】

We investigate systems of the form {A(t) g : g is an element of g, t is an element of [0, L]} where A is an element of B(4t) is a normal operator in a separable Hilbert space H, G subset of H is a countable set, and L is a positive real number. Although the main goal of this work is to study the frame properties of {A(t)g : g is an element of g, t is an element of[0, L]}, as intermediate steps, we explore the completeness and Bessel properties of such systems from a theoretical perspective, which are of interest by themselves. Beside the theoretical appeal of investigating such systems, their connections to dynamical and mobile sampling make them fundamental for understanding and solving several major problems in engineering and science. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free