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arXiv · 2201.09757

Frames via Unilateral Iterations of a Bounded Operator

Victor Bailey
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Abstract

Motivated by recent work in Dynamical Sampling, we prove a necessary and sufficient condition for a frame in a separable and infinite-dimensional Hilbert space to admit the form $\{T^{n} \varphi \}_{n \geq 0}$ with $T \in B(H)$. Also, a characterization of all the vectors $\varphi$ for which $\{T^{n} \varphi \}_{n \geq 0}$ is a frame for some $T \in B(H)$ is provided. Some auxiliary results on operator representations of Riesz frames are given as well.

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Victor Bailey. 2022-01-24. Frames via Unilateral Iterations of a Bounded Operator. https://arxiv.org/abs/2201.09757

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