Continuous and discrete dynamical sampling

In this paper we study the continuous dynamical sampling problem at infinite time in a complex Hilbert space H. We find necessary and sufficient conditions on a bounded linear operator A∈B(H) and a set of vectors G⊂H, in order to obtain that {etAg}g∈G,t∈[0,∞) is a semi-continuous frame for H. We stu...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2021-07, Vol.499 (2), p.125060, Article 125060
Main Authors: Díaz Martín, Rocío, Medri, Ivan, Molter, Ursula
Format: Article
Language:English
Subjects:
Continuous frame
Control theory
Dynamical sampling
Hardy space
Interpolating sequence
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Summary:In this paper we study the continuous dynamical sampling problem at infinite time in a complex Hilbert space H. We find necessary and sufficient conditions on a bounded linear operator A∈B(H) and a set of vectors G⊂H, in order to obtain that {etAg}g∈G,t∈[0,∞) 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 etA on a set G to the discrete iteration (A′)n on G′ for an adequate operator A′ and set G′⊂H.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2021.125060