Frames via Unilateral Iterations of a Bounded Operator
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866914855042154496 |
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| author | Bailey, Victor |
| author_facet | Bailey, Victor |
| contents | 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 $\{T^{n} φ\}_{n \geq 0}$ with $T \in B(H)$. Also, a characterization of all the vectors $φ$ for which $\{T^{n} φ\}_{n \geq 0}$ is a frame for some $T \in B(H)$ is provided. Some auxiliary results on operator representations of Riesz frames are given as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_09757 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Frames via Unilateral Iterations of a Bounded Operator Bailey, Victor Functional Analysis 46C99, 47A99 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 $\{T^{n} φ\}_{n \geq 0}$ with $T \in B(H)$. Also, a characterization of all the vectors $φ$ for which $\{T^{n} φ\}_{n \geq 0}$ is a frame for some $T \in B(H)$ is provided. Some auxiliary results on operator representations of Riesz frames are given as well. |
| title | Frames via Unilateral Iterations of a Bounded Operator |
| topic | Functional Analysis 46C99, 47A99 |
| url | https://arxiv.org/abs/2201.09757 |