Continuous and discrete dynamical sampling

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:499

Article

Diaz Martin, Rocio^1,2  Medri, Ivan³  Molter, Ursula^4,5 

[1] Consejo Nacl Invest Cient & Tecn, IAM, Saavedra 15, Caba, Argentina

[2] Univ Nacl Cordoba, Cordoba, Argentina

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

[4] Univ Buenos Aires, FCEyN, Dept Matemat, Caba, Argentina

[5] IMAS CONICET UBA, Caba, Argentina

关键词: Dynamical sampling;    Continuous frame;    Control theory;    Interpolating sequence;    Hardy space;   

DOI  :  10.1016/j.jmaa.2021.125060

来源: Elsevier

【 摘 要 】

In this paper we study the continuous dynamical sampling problem at infinite time in a complex Hilbert space IL We find necessary and sufficient conditions on a bounded linear operator A is an element of B(7-1) and a set of vectors g subset of 74, in order to obtain {e(tA)g}(g is an element of g, t is an element of[0, infinity)) is a semi-continuous frame for H. We study if it is possible to discretize the time variable t and still have a frame for H. We also relate the continuous iteration e(tA) on a set g to the discrete iteration (A')(n) on g' for an adequate operator A' and set g' subset of H. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free